System and method for identifying operational parameters of a motor

ABSTRACT

A system and method for establishing estimated values of electrical parameters of a motor. The electrical parameters may be established from stator resistance data and motor data obtained at a single load on the motor. The electrical parameters also may be established without stator resistance data by using motor data at three load conditions of the motor. The electrical parameters also may be established from baseline motor data and motor data obtained at a desired operating load of the motor. Based on the estimated values, the system and method also may be used to estimate motor operating parameters, such as torque, efficiency, output power, output speed, and other performance criteria of the motor.

BACKGROUND OF THE INVENTION

The present technique relates generally to the field of electric motors.More particularly, the invention relates to a novel technique forestimating unknown parameters of an induction motor based on motor dataobtained at one or more operating points or a no-load operating point.

A wide variety of induction motors are available and are currently inuse throughout a range of industrial applications. In general, suchmotors include a stator provided in a motor housing and a rotorsurrounded at least partially by the stator and supported for rotationwithin the housing. The stator and rotor may be mechanically andelectrically configured in a variety of manners depending upon a numberof factors, including: the application, the power available to drive themotor, and so forth. In general, however, electric power is applied tothe stator to produce a rotating magnetic field to drive the rotor inrotation. Mechanical power is transmitted from the motor via an outputshaft coupled to the rotor.

Motor operating parameters, such as output torque or efficiency, mayonly be determined with the motor in operation. Knowledge of these motoroperating parameters can be important for a number of reasons. However,the devices used to measure motor operating parameters may interferewith the operation of the motor or may be relatively expensive. Inaddition, it may be difficult to measure the operating parameter. Forexample, it may be desirable to maintain the temperature of the rotorbelow a specific temperature. However, it is extremely difficult tomeasure the rotor temperature. In addition, it may be desirable toestablish the torque and/or efficiency of a given motor to ensure thatthe proper motor is used in a given application. However, a typicaltorque measuring device requires the motor to be disconnected from itsload each time the torque measurement is desired, interferingsignificantly with the operation of the motor. Previous attempts todevelop a device to estimate motor operating parameters, such as torqueand efficiency, have relied on motor nameplate data. However, theseattempts have not yielded accurate results. Alternatively, a customermay not have the values of the motor electrical parameters that might beused to develop an estimate of various motor operating parameters.

A need exists for a technique for obtaining electric motor operatingparameter data that is less expensive than conventional methods andwhich minimizes the disruption to the operation of a systemincorporating the electric motor.

SUMMARY OF THE INVENTION

The present technique provides a novel system and method forestablishing estimated values of electrical parameters of a motor. Theelectrical parameters may be established from stator resistance data andmotor data obtained at a single load on the motor. The electricalparameters also may be established without stator resistance data byusing motor data at three load conditions of the motor. The electricalparameters also may be established from baseline motor data and motordata obtained at a desired operating load of the motor. Based on theestimated values, the system and method also may be used to estimatemotor operating parameters, such as torque, efficiency, output power,output speed, and other performance criteria of the motor.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other advantages and features of the invention willbecome apparent upon reading the following detailed description and uponreference to the drawings in which:

FIG. 1 is a perspective view of an electric motor illustrating thevarious functional components of the motor including a rotor and astator, in accordance with certain aspects of the invention;

FIG. 2 is the single-phase steady state equivalent schematic circuit ofan induction motor, according to an exemplary embodiment of the presenttechnique;

FIG. 3 is a system for providing estimated values of various motoroperating parameters, according to an exemplary embodiment of thepresent technique;

FIG. 4 is a process for providing estimated values of various motoroperating parameters based on data obtained at two load conditions ofthe motor, according to an exemplary embodiment of the presenttechnique;

FIG. 5 is an alternative equivalent schematic circuit of a steady stateinduction motor, according to an exemplary embodiment of the presenttechnique;

FIG. 6 is an alternative process for providing estimated values ofvarious motor operating parameters based on data obtained with no-loadon the motor, according to an exemplary embodiment of the presenttechnique;

FIG. 7 is another alternative process for providing estimated values ofvarious motor operating parameters based on data obtained at a singleload on the motor, according to an exemplary embodiment of the presenttechnique;

FIG. 8 is further alternative process for providing estimated values ofvarious motor operating parameters based on data obtained at first,second, and third loads on the motor, according to an exemplaryembodiment of the present technique;

FIG. 9 is another alternative process for providing estimated values ofvarious motor operating parameters based on baseline motor parametersand data obtained at a desired operating load on the motor, according toan exemplary embodiment of the present technique; and

FIG. 10 is a system for providing estimated values of various motoroperating parameters, according to an exemplary embodiment of thepresent technique.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

Turning now to the drawings, and referring first to FIG. 1, an electricmotor is shown and designated generally by the reference numeral 20. Inthe embodiment illustrated in FIG. 1, motor 20 is an induction motorhoused in a conventional NEMA enclosure. Accordingly, motor 20 includesa frame 22 open at front and rear ends and capped by a front end cap 24and a rear end cap 26. The frame 22, front end cap 24, and rear end cap26 form a protective shell, or housing, for a stator assembly 28 and arotor assembly 30. Stator windings are electrically interconnected toform groups, and the groups are, in turn, interconnected. The windingsare further coupled to terminal leads 32. The terminal leads 32 are usedto electrically connect the stator windings to an external power cable(not shown) coupled to a source of electrical power. Energizing thestator windings produces a magnetic field that induces rotation of therotor assembly 30. The electrical connection between the terminal leadsand the power cable is housed within a conduit box 34.

In the embodiment illustrated, rotor assembly 30 comprises a cast rotor36 supported on a rotary shaft 38. As will be appreciated by thoseskilled in the art, shaft 38 is configured for coupling to a drivenmachine element (not shown), for transmitting torque to the machineelement. Rotor 36 and shaft 38 are supported for rotation within frame22 by a front bearing set 40 and a rear bearing set 42 carried by frontend cap 24 and rear end cap 26, respectively. In the illustratedembodiment of electric motor 20, a cooling fan 44 is supported forrotation on shaft 38 to promote convective heat transfer through theframe 22. The frame 22 generally includes features permitting it to bemounted in a desired application, such as integral mounting feet 46. Aswill be appreciated by those skilled in the art, however, a wide varietyof rotor configurations may be envisaged in motors that may employ thetechniques outlined herein, including wound rotors of the type shown,and so forth. Similarly, the present technique may be applied to avariety of motor types having different frame designs, mounting andcooling styles, and so forth.

Referring generally to FIG. 2, an equivalent circuit for steady stateoperation of the induction motor of FIG. 1 is shown and designatedgenerally by the reference numeral 50. The induction motor is powered byan AC power source, designated by reference numeral 52, having a voltageamplitude V₁ and a frequency ω. The stator of the motor has anelectrical resistance R₁, as represented by reference numeral 54, and aleakage inductance L₁, as represented by reference numeral 56. The motoralso has core loss resistance R_(c) due to core losses in the stator androtor, designated by the reference numeral 58. The motor also has amagnetizing inductance L_(m), designated by reference numeral 60. Therotor also has an electrical resistance R₂, designated by referencenumeral 62. As illustrated, the rotor resistance R₂ is modified bydividing the rotor resistance R₂ by the slip s of the rotor. Finally,the rotor also has a leakage inductance L₂, as represented by referencenumeral 64. Electric current flows through the stator to produce themagnetic field. The electric current I₁ through the stator isrepresented by arrow 66. In addition, the magnetic field induces anelectric current I₂ in the rotor, as represented by arrow 68. Finally,electric current I₃ flowing through the core loss resistance R_(c) andthe magnetizing inductance L_(m) is represented by arrow 70.

In a typical AC circuit, the voltage and current vary over time. In aninductive circuit, such as an induction motor, the voltage leads thecurrent by an angle, known as the phase angle φ. In addition, some poweris alternately stored and released by the inductance of the circuit.This power is known as the “reactive power.” In addition, the resistanceof the circuit dissipates power as heat and the load utilizes a portionof the input power, this power is known as the “real power.” The“apparent power” is the product of the total voltage and the totalcurrent in the AC circuit. The ratio between the real power and theapparent power of a load in an AC circuit is known as the “power factor”of the load. The cosine of the phase angle is the power factor.

Referring generally to FIG. 3, a system for providing estimated valuesof various motor electrical parameters and motor operating parameters isshown and designated generally by reference numeral 80. The system 80comprises a data processing module 82 that is electrically coupleable tothe motor 20. The data processing module 82 is operable to utilize dataobtained at two load conditions of the motor 20 to establish values ofvarious electrical parameters of the motor, such as the electricalresistance of the rotor and the leakage inductance of the stator androtor. The data processing module then uses the values of the estimatedmotor electrical parameters to estimate motor operating parameters, suchas the temperature of the rotor, the torque of the motor, and theefficiency of the motor. The data processing module 82 may be providedas a stand-alone device, as part of a motor, or in a kit form to beadded to an existing installed motor.

In the illustrated embodiment, the data processing module 82 has aprocessor module 84. Preferably, the processor module 84 utilizes aprocessor (not shown) and operates in accordance with programminginstructions to produce estimates of various motor operating parameters.The processor module 84 may have analog-to-digital converters forconverting analog data into digital data. In this embodiment, theprocessor module 84 is electrically coupled to each phase 86 of theinput power to the motor 28 to enable the module to receive electricalinput data, such as the input voltage, current, frequency, and power.However, the data also may be entered into the system manually. Theinput voltage data may be the line-to-line voltage or the phase voltage.The average phase voltage for a connection may be established byaveraging the three line-to-line voltages and dividing by the {squareroot}{square root over (3)}. The average line current is the phasecurrent. Input power data also may be obtained directly or calculatedfrom the stator voltage, current, and resistance data. A speed sensor 88also is electrically coupled to the processor module 84. The speedsensor 88 may be integral with the motor or a separate device coupled tothe processor module 84. The speed sensor 88 may measure the speed ofthe shaft 38 coupled to the rotor 36 in order to establish rotor speed.Alternatively, the speed sensor 88 may measure the speed of the rotor 36directly.

In the illustrated embodiment, the system 80 is operable to output motorelectrical parameter data and motor operating parameter data to acontrol module 90. Preferably, the control module 90 has a visualdisplay 92 to provide visual indications of the various parameters.Preferably, the control module 90 has a keypad or keyboard 94 to enabledata, such as the electrical input data, rotor speed data, and any knownmotor electrical parameters, to be inputted into the processor module84. In addition, in the illustrated embodiment the processor module 84and the control module 90 are coupled to a network 96 to enable data tobe transferred to or from remote terminals 98. The remote terminals 98may be personal computers, or other digital communication devices.

The electrical input data may also be measured at the motor controller,rather than at the motor itself. However, in certain applications themotor controller may be quite remote from the motor. To facilitate themeasurement of data at the motor, such as the rotor speed, and at otherlocations, such as at a motor controller, a time log of the measuredvoltages, currents, power and frequency may be used to record data. Thevoltages, currents, power and frequency corresponding to the time of thespeed measurement are retrieved from the time log and matched to thespeed of the rotor at that time. An adjustment also can be provided forthe effect on the electrical input data caused by taking the measurementat the motor controller. First, the length of the cable between themotor and the starter may be measured. In addition, the ambienttemperature is measured and the gauge of the cable identified. Thediameter of the conductor may be calculated from the gauge of the cable.The resistance of the cable may be estimated based on the operatingtemperature, the length and diameter of the cable. The cable resistanceis then subtracted from the total measured resistance to establish thestator resistance. Furthermore, the power loss in the cable may beestablished from the measured current and estimated cable resistance.The cable power is then subtracted from the measured power to obtain thepower delivered to the motor.

Referring generally to FIG. 4, a process for establishing values ofvarious motor electrical parameters and various motor operatingparameters using the system of FIG. 3 is shown and designated generallyby reference numeral 100. The process comprises obtaining the resistanceof the stator, as represented by block 102. The process also comprisesobtaining data at a first operating load point and providing the data tothe processor module 84, as represented by block 104. In a presentlycontemplated embodiment, the data obtained at the first load pointcomprises: input voltage data, input current data, input power data, andshaft speed data. It should be noted that the input power can either bemeasured or calculated from the other input data. In addition, theprocess may measure motor frequency and temperature. Some data may beprovided to the system 80 using the control module 90 or may be providedfrom a remote station 98 via the network 96. Preferably, the motor has alow load at the first operating point.

The process also comprises obtaining data from the motor at a secondload point and providing the data to the processor module 84, asrepresented by block 106. The stator resistance R₁ data need only beobtained once if the stator temperature is obtained at each load point.Preferably, the motor has a full load at the second load point.

The data processing module 82 may then be operated to establishestimated values of various motor parameters, as represented by block108. The programming instructions provided to the data processing module82 are adapted to utilize a novel technique for establishing the valuesof the various motor parameters. The equivalent circuit of FIG. 2provides a starting point to illustrate the development of the techniquefor estimating various motor parameters. Referring generally to FIG. 5,an equivalent circuit, designated generally by reference numeral 110, tothe circuit of FIG. 2 is illustrated. In FIG. 5, each inductanceillustrated in FIG. 2 is converted into an inductive reactance tofacilitate solving for the unknown motor parameters. In addition, someof the reactances are combined to simplify the circuit 110. The statorleakage reactance X₁, designated by reference numeral 112, is a functionof the electrical frequency ω of the power source and the stator leakageinductance L₁. The equivalent reactance X_(e), designated by referencenumeral 114, is a function of the magnetizing reactance X_(m), the rotorresistance R₂, the slip s and the rotor leakage reactance X₂. Themagnetizing reactance X_(m), in turn, is a function of the electricalfrequency ω and the magnetizing inductance L_(m). The rotor leakagereactance X₂ is a function of the electrical frequency ω and the rotorleakage inductance L₂. The equivalent resistance R_(e), designated byreference numeral 116, is a function of the rotor resistance R₂, theleakage reactance X₂, the slip s, and the core loss resistance R_(c). Ofthe parameters illustrated in FIGS. 2 and 5, the stator resistance R₁and the motor slip s can be measured relatively easily. This leaves thevalues of five parameters to be established: X₁, R₂, X₂, R_(c), andX_(m). These parameters are more difficult to measure than the statorresistance R₁ and the motor slip s.

Several assumptions and an approximation are made to simplify theprocess of developing a technique for estimating X₁, R₂, X₂, R_(c), andX_(m). Namely, it is assumed that the frequency of the power isconstant, that the speed of the rotor does not change during thegathering of the load point data, and that the reading of the data isdone quickly so that the rotor temperature is constant during thegathering of the data. Additionally, it has been establishedexperimentally that excellent results are obtained by estimating thestator leakage reactance X₁ to be 5% of the magnetizing reactance X_(m),or:X ₁=0.05X _(m).  (1)However, this factor may range from 0.02 to 0.07. By making thisapproximation the number of unknowns is reduced to four. Thus, only fourequations are needed to solve for the values of the remaining unknownmotor parameters. However, the equations relating these unknowns arehighly nonlinear and an expression for the remaining unknowns by usingmeasurements obtained at two load points is nontrivial. In the presenttechnique, this process is facilitated by obtaining an actual value forthe stator leakage reactance X₁. This value is then used in finding thevalues of the remaining unknowns.

In addition, the rotor leakage inductance L₂ and magnetizing inductanceL_(m) are converted into reactances in FIG. 5 to assist in solving thevarious unknown motor parameters. Reactance is a function of theinductance and the frequency ω of the circuit. The reactances werecombined with the rotor resistance R₂ and the core loss resistance R_(c)to form an equivalent reactance X_(e) and a total resistance R_(t). At afirst load point, the total resistance R_(t1) is given by the followingequation: $\begin{matrix}{\frac{1}{R_{t1}} = {\frac{1}{R_{c}} + {\frac{1}{\left( {\frac{R_{2}}{s_{1}} + \frac{s_{1}X_{2}^{2}}{R_{2}}} \right)}.}}} & (2)\end{matrix}$

The first term on the right side of the equation is the reciprocal ofthe core loss resistance R_(c) and the second term is the reciprocal ofthe new modified rotor resistance as a result of factoring the rotorleakage reactance X₂. At the second load point, the total resistanceR_(t2) is given by the following equation: $\begin{matrix}{\frac{1}{R_{r2}} = {\frac{1}{R_{c}} + {\frac{1}{\left( {\frac{R_{2}}{s_{2}} + \frac{s_{2}X_{2}^{2}}{R_{2}}} \right)}.}}} & (3)\end{matrix}$

Similarly, the equivalent reactances at the two motor load points X_(e1)and X_(e2) are given by the following equations: $\begin{matrix}{{\frac{1}{X_{e1}} = {\frac{1}{X_{m}} + \frac{X_{2}}{\left( {\frac{R_{2}^{2}}{s_{1}^{2}} + X_{2}^{2}} \right)}}};{and}} & (4) \\{\frac{1}{X_{e2}} = {\frac{1}{X_{m}} + {\frac{X_{2}}{\left( {\frac{R_{2}^{2}}{s_{2}^{2}} + X_{2}^{2}} \right)}.}}} & (5)\end{matrix}$The right hand sides of equations (4) and (5) also have two terms, oneresulting from the magnetizing reactance X_(m) and the other resultingfrom factoring the rotor leakage reactance X₂.

The following equations for equivalent reactance X_(e) and equivalentresistance R_(e) may be developed using FIG. 5 and data obtained at thetwo load points of the motor. The equation for the equivalent reactanceX_(e) is given as follows: $\begin{matrix}{{X_{e} = {\frac{- B}{2A} + \frac{\sqrt{B^{2} - {4{AC}}}}{2A}}},} & (6)\end{matrix}$where A, B, and C are given by:A=1.05*0.05*sI ₁ ²;  (7)B=−1.1I ₁ V _(1i) s; and  (8)C=V _(1i) ² s+(sR ₁ I ₁ −sV _(1R))(I ₁ R ₁ −V _(1R)).  (9)V_(1i) is the imaginary portion of the voltage and is a function of theamplitude of the power source voltage V₁ and the sine of the powerfactor angle. V_(1R) is the real portion of the voltage and is afunction of the amplitude of the power source voltage V₁ and the cosineof the phase angle. In addition, the equivalent resistance R_(e) isgiven by the following equation: $\begin{matrix}{R_{e} = {\frac{{sX}_{e}\left( {V_{1j} - {{.05}I_{1}X_{e}}} \right)}{\left( {V_{1R} - {I_{1}R_{1}}} \right)}.}} & (10)\end{matrix}$

As discussed above, it was assumed that the stator leakage reactance is5%, or 0.05 of the magnetizing reactance X_(m). With no load on themotor, the rotor section of the circuit is considered open and the valuefor the slip s is considered to be zero. The total reactance of thecircuit is made of the sum of the stator leakage reactance X₁ and themagnetizing reactance X_(m). Since X₁ can be expressed as equal to0.05X_(m), then the total no-load reactance can be written as 1.05X_(m).The value of X_(e) at the two load points is used to extrapolate thevalue at no-load to yield X_(m). The value of X_(e) at zero-load is themagnetizing reactance X_(m). In addition, the slip s is used as ameasure of the load. Through experimentation using different load pointsand different motors, it has been found that the following equationyields a very close value for the magnetizing reactance X_(mi) to beused for estimating the stator leakage reactance X₁: $\begin{matrix}{X_{mi} = {X_{e1} + {\frac{\left( {X_{e2} - X_{e1}} \right)s_{1}^{\frac{1}{4}}}{\left( {s_{1} - s_{2}} \right)^{\frac{1}{4}}}.}}} & (11)\end{matrix}$

In equation (11) above, s₁ is the slip at a high load and s₂ is the slipat a low load, noting that s₁ is greater than s₂. The value of X_(mi)may then be used to establish the value of X₁, in accordance withequation (1) provided above.

Once the value of X₁ is obtained, new values for R_(t) and X_(e) may beobtained. These new values of R_(t) and X_(e) are based on a fixed knownvalue of the stator reactance X₁, and may be determined in accordancewith the following equations: $\begin{matrix}{{\alpha_{1} = {\frac{1}{R_{t1}} - \frac{1}{R_{t2}}}};{and}} & (12) \\{\alpha_{2} = {\frac{1}{X_{e1}} - {\frac{1}{X_{e2}}.}}} & (13)\end{matrix}$

There now are four equations and four unknowns. The unknowns are R₂, X₂,R_(c), and X_(m). To eliminate R_(c), equation (3) is subtracted fromequation (2) to yield the following equation: $\begin{matrix}{\alpha_{1} = {\frac{{\frac{R_{2}}{s_{1}}\left( {\frac{R_{2}^{2}}{s_{2}^{2}} + X_{2}^{2}} \right)} - {\frac{R_{2}}{s_{2}}\left( {\frac{R_{2}^{2}}{s_{1}^{2}} + X_{2}^{2}} \right)}}{\left( {\frac{R_{2}^{2}}{s_{1}^{2}} + X_{2}^{2}} \right)\left( {\frac{R_{2}^{2}}{s_{2}^{2}} + X_{2}^{2}} \right)}.}} & (14)\end{matrix}$To eliminate X_(m), equation (5) is subtracted from equation (4)yielding the following equation: $\begin{matrix}{\alpha_{2} = {\frac{{X_{2}\left( {\frac{R_{2}^{2}}{s_{2}^{2}} + X_{2}^{2}} \right)} - {X_{2}\left( {\frac{R_{2}^{2}}{s_{1}^{2}} + X_{2}^{2}} \right)}}{\left( {\frac{R_{2}^{2}}{s_{1}^{2}} + X_{2}^{2}} \right)\left( {\frac{R_{2}^{2}}{s_{2}^{2}} + X_{2}^{2}} \right)}.}} & (15)\end{matrix}$

From the equations provided above, equations may now be established forR₂, X₂, R_(c), and X_(m). By dividing equation (14) by equation (15),the following relationship for the X₂ and R₂ can be established:X ₂ =γR ₂.  (16)where γ is given by the following equation: $\begin{matrix}{\gamma = {\frac{- {\alpha_{1}\left( {s_{1} + s_{2}} \right)}}{2\quad\alpha_{2}s_{1}s_{2}} + {\frac{\sqrt{{\left( \frac{\alpha_{1}}{\alpha_{2}} \right)^{2}\left( {s_{1} + s_{2}} \right)^{2}} + {4s_{1}s_{2}}}}{2s_{1}s_{2}}.}}} & (17)\end{matrix}$The rotor resistance R₂ may be established by substituting γR₂ for X₂ inequation (15) and using algebraic manipulation to produce the followingequation: $\begin{matrix}{R_{2} = {\frac{\frac{\gamma}{\alpha_{2}}}{\left( \frac{1}{s_{1}^{2} + \gamma^{2}} \right)} - {\frac{\frac{\gamma}{\alpha_{2}}}{\left( \frac{1}{s_{2}^{2} + \gamma^{2}} \right)}.}}} & (18)\end{matrix}$In addition, the core loss resistance R_(c) may be established in termsof R₂ and X₂ by manipulating equation (2) to produce the followingequation: $\begin{matrix}{R_{c} = \frac{1}{\left( {\frac{1}{R_{t1}} - \frac{\frac{R_{2}}{s_{1}}}{\left( {\frac{R_{2}^{2}}{s_{1}^{2}} + X_{2}^{2}} \right)}} \right)}} & (19)\end{matrix}$Finally, the magnetizing reactance X_(m) may be established in terms ofR₂ and X₂ by manipulating equation (4) to produce the followingequation: $\begin{matrix}{X_{m} = {\frac{1}{\left( {\frac{1}{X_{e1}} - \frac{X_{2}}{\left( {\frac{R_{2}^{2}}{s_{1}^{2}} + X_{2}^{2}} \right)}} \right)}.}} & (20)\end{matrix}$

The data processing module 82 is programmed to use the above-describedequations and methodology to establish estimated values of rotorresistance R₂, leakage reactance X₂, core loss resistance R_(c), andmagnetizing reactance X_(m). Voltage and current input data are obtainedat the two load points and provided to the processor module 84. Inputpower data also may be obtained at the same two points or calculatedfrom the voltage, current, and/or resistance data. In addition, motorspeed data also is provided to the data processing module 82. The motorspeed data may be the RPM of the motor or the slip. Ideally, themeasurements at the two load points are made simultaneously to avoidpotential change due to a change in the operating condition of themotor. In addition, in the illustrated embodiment the line-to-lineelectrical resistance of the stator is provided to the processor. Thephase resistance is established by averaging the line-to-line resistanceand dividing by 2. The data processing module 82 is operable toestablish the value of the equivalent reactances X_(e1) and X_(e2) usingequations (6) through (10) provided above at each load point. Theprocessor also is operable to establish the initial magnetizingreactance X_(mi) using equation (11) provided above. In addition, theprocessor is operable to establish the value of the phase leakagereactance X₁ from the magnetizing reactance X_(mi). Using the value ofX₁, the processor is operable to find new values for the equivalentresistances R_(t1), R_(t2), X_(e1), and X_(e2), where: $\begin{matrix}{{R_{t1} = \frac{R_{e1}}{s_{1}}};{and}} & (21) \\{R_{t2} = {\frac{R_{e2}}{s_{2}}.}} & (22)\end{matrix}$

The system may also be operated to estimate motor operating parametersbased on the values of X₁, R₂, X₂, R_(c), and X_(m), as represented byblock 118. For example, the system may be adapted to establish thevalues of the rotor torque T, the rotor temperature, and the motorefficiency based on the values of R₂, X₂, R_(c), and X_(m), electricalinput data and rotor speed data. The rotor current I₂ may be establishedusing the following equation: $\begin{matrix}\begin{matrix}{I_{2} = {\left( {I_{1} - \frac{\left( {V_{1R} - {I_{1}R_{1}}} \right)}{R_{c}} - \frac{\left( {V_{1i} - {I_{1}X_{1}}} \right)}{X_{m}}} \right) +}} \\{{j\left( {\frac{\left( {V_{1R} - {I_{1}R_{1}}} \right)}{X_{m}} - \frac{\left( {V_{1i} - {I_{1}X_{1}}} \right)}{R_{c}}} \right)}.}\end{matrix} & (23)\end{matrix}$

The shaft torque may be obtained from the rotor resistance R₂ and therotor current I₂, as follows: $\begin{matrix}{{T\left( {N - m} \right)} = {\frac{3I_{2{rms}}^{2}R_{2}}{\omega_{s}s}.}} & (24)\end{matrix}$In the above equation, I_(2rms) is the RMS value of the rotor currentI₂, and ω_(s) is the mechanical synchronous speed in rad/second givenby: $\begin{matrix}{\omega_{s} = {\frac{4\quad\pi\quad f}{p}.}} & (25)\end{matrix}$

In this equation, f is the alternating current frequency in Hz and p isthe number of poles of the motor.

The shaft torque may be converted to foot-pounds by multiplying thetorque in Newton-meters by 0.738. In addition, the shaft torque ismodified by subtracting the friction and windage loss R_(F&W) and thestray load loss using published values and IEEE standards, as shown inthe following table: Motor Power SLL % of output power   1-125 HP 1.8 126-500 HP 1.5 501-2499 HP 1.2

The motor efficiency is established by dividing the estimated outputmechanical power by the input electrical power. $\begin{matrix}{\eta = {\frac{P_{out}}{P_{in}}.}} & (26)\end{matrix}$The estimated output mechanical power P_(out) may be established fromthe torque T and the rotor speed data.

The above-described technique was used to estimate the efficiency of a10 HP motor and a 600 HP motor using data from a motor design programand test data. The following are the results obtained for a 10 HP motorand the discussion of these results. Motor Data: HP: 10 Elec. Des.:E9893A A RPM: 1175 Frame: 0256T Enclosure: TEFC Design: B Volts: 575 LRCode: G Amp: 10.1 Rotor: 418138071HE Duty: Cont. Stator: 418126002AJINS/AMB/S.F.: F/40/1.15 FAN: 702675001A TYP/PH/HZ: P/3/60

Using data from the program at full load and at ¼ load, the parametersof the motor were identified using the new method. The following is asummary of the results. Estimated Efficiency Program Efficiency % ErrorFull Load 91.315 91.097 0.239% ¾ Load 92.154 91.850 0.330% ½ Load 92.10191.661 0.479% ¼ Load 89.005 88.186 0.928%

From the above results it can be seen that the error in the estimatedefficiency is less than 1% of the efficiency obtained from the programresults. It can also be observed that the error increases as the loaddecreases. By examining the calculated losses it was noticed that thecalculated core loss is less than the program value by 19 watts. Thisfixed error becomes a larger percentage of the total loss at low loadsand as a result the percentage error in efficiency increases as the loaddecreases.

The estimated efficiency was also compared to laboratory test data. Thefollowing is a summary of the results for the 10 HP motor. EstimatedEfficiency Actual Efficiency % Error Full Load 89.98 90.310 −0.36% ¼Load 86.18 86.530 −0.41%The estimated core loss in this case was more than the measured valueleading to a lower estimated efficiency than the measured efficiency.

The procedure was repeated for a 600 HP motor. The following are theresults obtained for a 600 HP motor and the discussion of these results.Motor Data: HP: 600 Elec. Des.: RPM: 1195 Frame: 35C5012Z Enclosure:TEFC Design: 139481 Volts: 575 LR Code: Amp: 532 Rotor: 710623-2-S Duty:Cont. Stator: 710622-2-T INS/AMB/S.F.: F/ /1.15

Comparing the design program data to the estimated values from theabove-described process, the following results were obtained: EstimatedEfficiency Program Efficiency % Error Full Load 95.794 95.791 0.003% ¾Load 95.843 95.855 −0.013% ½ Load 95.318 95.352 −0.035% ¼ Load 92.65592.710 −0.059%The difference between the design program data and estimated value datais less 0.04%. Initially, the resolution selected for use with thedesign program data for the speed of the motor was one decimal point.The results obtained using one decimal point resolution on speed lead tohigher error in estimation. The results provided above were obtainedusing a higher resolution on speed. In addition, this particular motorhas a very low slip. The slip in RPM at full load is less than 5 RPM sothat any error in the speed measurement will lead to a large error inestimation. The following are the results obtained using four decimalpoints resolution, three decimal points resolution, two decimal pointsand one decimal point resolution to illustrate the effect of resolutionon the efficiency estimation.

Four Decimal Points Resolution: Estimated Efficiency Program Efficiency% Error Full Load 95.795 95.791 0.0036% ¾ Load 95.844 95.855 −0.0122% ½Load 95.320 95.352 −0.0338% ¼ Load 92.658 92.710 −0.0550%

Three Decimal Points Resolution: Estimated Efficiency Program Efficiency% Error Full Load 95.797 95.791 0.0065% ¾ Load 95.848 95.855 −0.008% ½Load 95.325 95.352 −0.028% ¼ Load 92.669 92.710 −0.044%

Two Decimal Points Resolution: Estimated Efficiency Program Efficiency %Error FullLoad 95.887 95.791 −0.0143% ¾ Load 95.969 95.855 −0.0364% ½Load 95.509 95.352 −.0705% ¼ Load 93.031 92.710 −0.1297%

One Decimal Point Resolution: Estimated Efficiency Program Efficiency %Error Full Load 95.008 95.791 −0.817% ¾ Load 94.776 95.855 −0.840% ½Load 93.708 95.352 −1.200% ¼ Load 89.494 92.710 −3.486%

From the above results it can be concluded that to provide a goodestimation of efficiency for low slip motors using this method it ispreferable to have a resolution on speed to at least two decimal points.The reason for this is that if the resolution is less than two decimalpoints the error in slip causes an error in the estimation of the coreloss, yielding a higher overall error.

The system was then operated using lab test data for the 600 HP motor.The resolution of the speed that was used was 1 RPM. This resolution isless than the minimum recommended for obtaining good results. Theresults using this coarse resolution are shown below. EstimatedEfficiency Program Efficiency % Error Full Load 96.59 96.65 −0.052% ¾Load 95.87 96.68 −0.840% ½ Load 95.02 96.17  −1.20% ¼ Load 95.95 93.62 2.480%From these results, it can be concluded that the method yields excellentresults for regular slip motors. However, for low slip motors theresolution on the RPM of the motor is preferably at least two decimalpoints so as to get a good estimate of the motor efficiency in thefield. One way of obtaining excellent resolution of the motor speed isby using accelerometers to measure the motor vibration and find itsspectrum.

A comparison between the losses seen in the design program and theestimated losses using the above-described method is provided below.Design Program New Method Rotor Loss: Full Load 1.79 KW 1.785 KW ¾ Load.980 KW  .979 KW ½ Load .430 KW  .429 KW ¼ Load .107 KW  .107 KW CoreLoss: Full Load 5.77 KW 5.756 KW ¾Load 5.81 KW 5.852 KW ½ Load 5.85 KW5.924 KW ¼ Load  5.9 KW 5.975 KWThe results illustrate general agreement between the design programresults and the new method of estimating motor parameters describeabove.

Referring generally to FIG. 6, an alternative process for establishingestimated values of various motor electrical parameters using dataobtained at a single operating point with no load on the motor is shownand designated generally by reference numeral 120. In addition, theestimated values of the motor electrical parameters may be used toestablish estimated values of various motor operating parameters. Theprocess comprises obtaining stator resistance R₁ data, as represented byblock 122. The line-to-line input resistance may be measured, averaged,and divided by 2 to determine the phase resistance R₁. The process alsocomprises obtaining electrical input data with no load on the motor andproviding the data to the processor module 84, as represented by block124. To achieve the no-load condition, the motor is disconnected fromits load. The electrical input data obtained at the first load pointscomprises: input voltage data, input current data. Some data may beprovided to the system 80 using the control module 90 or may be providedfrom a remote station 98 via the network 96. The current with no-loadI_(nl) may be measured for each phase and averaged. The three linevoltages may be measured, averaged, and divide by {square root}{squareroot over (3)} to determine the phase voltage V₁.

The data processing module 82 may then be operated to establishestimated values of various motor parameters, as represented by block126. The programming instructions are provided to the data processingmodule 82 are adapted to utilize a novel technique for establishing thevalues of the various motor parameters using data obtained with no-loadon the motor. With no load on the motor, the rotor portion of thecircuit will effectively be an open circuit and is assumed to be an opencircuit for these purposes. The current I₂ will be sufficiently small tohandle the windage and friction load of the rotor. With no load on themotor, the stator current I₁ will be the no-load current I_(nl). Thestator leakage inductance L₁, the magnetizing inductance L_(m) and thecore loss resistance R_(c) may be established using the followingequations. First, the total resistance R_(t) may be obtained by thefollowing equation: $\begin{matrix}{R_{t} = {\frac{P}{I_{nl}^{2}}.}} & (27)\end{matrix}$

The total impedance Z may be found by dividing the input voltage V₁ bythe no-load current I_(nl), as follows: $\begin{matrix}{Z = {\frac{V_{1}}{I_{nl}}.}} & (28)\end{matrix}$

The total reactance X₁+X_(m) may be found from the total impedance Z andthe total resistance R_(t), as follows:X ₁ +X _(m)={square root}{square root over (Z ² −R _(t) ²)}.  (29)

The individual values for the stator reactance X₁ and the magnetizingreactance X_(m) may be found from the assumed relationship of X₁=0.05X_(m), as follows:X ₁ +X _(m)=1.05X _(m).  (30)

Next, the motor friction and windage power P_(F&W) may be estimatedbased on the motor size and construction, if known. If not, the motorfriction and windage power P_(F&W) is combined with the core loss. Theequivalent resistance R_(W&F) due to motor friction and windage powerP_(F&W) may be estimated as follows: $\begin{matrix}{R_{{W\&}F} = {\frac{P_{{W\&}F}}{I_{nl}^{2}}.}} & (31)\end{matrix}$

The series core loss resistance R_(m), may be established as follows:R _(m) =R _(t) −R ₁ −R _(W&F).  (32)

The parallel magnetizing inductance L_(m), may be established asfollows: $\begin{matrix}{L_{m} = {\frac{X_{m}^{2} + R_{m}^{2}}{X_{m}\omega}.}} & (33)\end{matrix}$

The parallel core resistance R_(c), may be established as follows:$\begin{matrix}{R_{c} = {\frac{X_{m}^{2} + R_{m}^{2}}{R_{m}}.}} & (34)\end{matrix}$

The stator leakage inductance L₁, may be established as follows:$\begin{matrix}{L_{1} = {\frac{X_{1}}{\omega}.}} & (35)\end{matrix}$

As with the previous two load point method, the data processing module82 may be used to estimate other motor parameters based on the estimatedmotor electrical parameter data obtained above, as represented by block128. An expression of the rotor current I₂ may be obtained from thevoltage across the rotor and the rotor impedance. Designating thevoltage across the rotor as V_(a) and the rotor current as I₂, thefollowing equation can be written: $\begin{matrix}{I_{2} = {\frac{V_{a}}{\frac{R_{2}}{S} + {j\quad\omega\quad L_{2}}}.}} & (36)\end{matrix}$

The rotor current can also be expressed using the input current I₁, thecurrent through the magnetizing inductance I_(m), and the currentthrough the core resistance I_(c), as follows:I ₂ =I ₁ −I _(c) −I _(m).  (37)

The above currents can be expressed in terms of the voltage and thevalue of the motor parameters as follows:V _(a) =V ₁ −I ₁(R ₁ +jωL ₁);  (38) $\begin{matrix}{{I_{c} = \frac{V_{a}}{R_{c}}};{and}} & (39) \\{I_{m} = {\frac{V_{a}}{j\quad\omega\quad L_{m}}.}} & (40)\end{matrix}$

The following expression for I₂ may be obtained by manipulating theequations above and substituting the expressions for I₁, I_(c), andI_(m) from equations (38)-(40) into equation (37): $\begin{matrix}{I_{2} = {I_{1} - \frac{\left( {V_{1} - {I_{1}\left( {R_{1} + {j\quad\omega\quad L_{1}}} \right)}} \right)}{R_{c}} - {\frac{\left( {V_{1} - {I_{1}\left( {R_{1} + {j\quad\omega\quad L_{1}}} \right)}} \right.}{j\quad\omega\quad L_{m}}.}}} & (41)\end{matrix}$

Equations (36) and (41) can now be equated to obtain an equationrelating the input current, the input voltage, and the motor parameters.Because the resulting equation has a real part and imaginary part, thiswill yield two equations. The input current can be written as a complexquantity:I ₁ =I _(1R) −jI _(1i).  (42)

Two equations, one representing the real part and one representing theimaginary part, may be obtained using equations (34), (39) and (40). Thereal part is as follows: $\begin{matrix}{{\left( {I_{1R} - \frac{V_{1}}{R_{c}} + \frac{I_{1R}R_{1}}{R_{c}} + \frac{I_{1i}\omega\quad L_{1}}{R_{c}} + \frac{I_{1R}L_{1}}{L_{m}} - \frac{R_{1}I_{1i}}{\omega\quad L_{m}}} \right)\left( {\frac{R_{2}^{2}}{s^{2}} + {\omega^{2}L_{2}^{2}}} \right)} = {{\frac{R_{2}}{S}\left( {V_{1} - {I_{1R}R_{1}} - {I_{1i}\omega\quad L_{1}}} \right)} - {\omega\quad{{L_{2}\left( {{\omega\quad L_{1}I_{1R}} - {R_{1}I_{1i}}} \right)}.}}}} & (43)\end{matrix}$

The imaginary part will be given by: $\begin{matrix}{{\left( {{- I_{1i}} + \frac{\omega\quad L_{1}I_{1R}}{R_{c}} - \frac{R_{1}I_{1i}}{R_{c}} + \frac{V_{1}}{\omega\quad L_{m}} - \frac{I_{1R}R_{1}}{\omega\quad L_{m}} - \frac{I_{1i}L_{1}}{L_{m}}} \right) \cdot \left( {\frac{R_{2}^{2}}{s^{2}} + {\omega^{2}L_{2}^{2}}} \right)} = {{{- \frac{R_{2}}{s}}\left( {{\omega\quad L_{1}I_{1R}} - {R_{1}I_{1i}}} \right)} - {\omega\quad{{L_{2}\left( {V_{1} - {I_{1R}R_{1}} - {I_{1i}\omega\quad L_{1}}} \right)}.}}}} & (44)\end{matrix}$Equations 43 and 44 can be written as: $\begin{matrix}{{{\alpha_{1}\left( {\frac{R_{2}^{2}}{S^{2}} + {\omega^{2}L_{2}^{2}}} \right)} = {{\alpha_{2}R_{2}} + {\alpha_{3}L_{2}}}};{and}} & (45) \\{{{\beta_{1}\left( {\frac{R_{2}^{2}}{S^{2}} + {\omega^{2}L_{2}^{2}}} \right)} = {{\beta_{2}R_{2}} + {\beta_{3}L_{2}}}};} & (46)\end{matrix}$where the different variables are given by: $\begin{matrix}{{\alpha_{1} = {I_{1R} - \frac{V_{1}}{R_{c}} + \frac{I_{1R}R_{1}}{R_{c}} + \frac{I_{1i}\omega\quad L_{1}}{R_{c}} + \frac{L_{1}I_{1R}}{L_{m}} - \frac{R_{1}I_{1i}}{\omega\quad L_{m}}}};} & (47) \\{{\alpha_{2} = \frac{V_{1} - {I_{1R}R_{1}} - {I_{i1}\omega\quad L_{1}}}{s}};} & (48) \\{{\alpha_{3} = {- {\omega\left( {{\omega\quad L_{1}I_{1R}} - {R_{1}I_{1i}}} \right)}}};} & (49) \\{{\beta_{1} = {{- I_{1i}} + \frac{\omega\quad L_{1}I_{1R}}{R_{c}} - \frac{R_{1}I_{1i}}{R_{c}} + \frac{V_{1}}{\omega\quad L_{m}} - \frac{I_{1R}R_{1}}{\omega\quad L_{m}} - \frac{I_{1i}L_{1}}{L_{m}}}};} & (50) \\{{\beta_{2} = \frac{\alpha_{3}S}{\omega}};{and}} & (51) \\{\beta_{3} = {{- \alpha_{2}}\omega\quad{S.}}} & (52)\end{matrix}$

Dividing equations (43) and (44) and solving for the rotor inductance interms of the rotor resistance one gets: $\begin{matrix}{{L_{2} = {\gamma\quad R_{2}}};} & (53) \\{{\text{where:}\quad\gamma} = {\frac{{\alpha_{1}\beta_{2}} - {\alpha_{2}\beta_{1}}}{{\alpha_{3}\beta_{1}} - {\alpha_{1}\beta_{3}}}.}} & (54)\end{matrix}$

Solving for the rotor resistance, the following relationship results:$\begin{matrix}{R_{2} = {\frac{\frac{\alpha_{2}}{\alpha_{1}} + \frac{\alpha_{3}\gamma}{\alpha_{1}}}{{\omega^{2}\gamma^{2}} + {1/s^{2}}}.}} & (55)\end{matrix}$

The following process may be used for calculating motor torque and motorefficiency. First, estimate the slip s from the shaft speed N and thesynchronous speed N_(s), as follows: $\begin{matrix}{s = {\frac{N_{S} - N}{N_{S}}.}} & (56)\end{matrix}$

The synchronous speed Ns may be obtained from the input frequency andthe number of poles of the motor. The power factor may then be computedusing the input current, input voltage, and input power.

Next, the real and imaginary components of the current I_(1R) & I_(1i)are established using equations (47-54). The rotor resistance may thenbe established using the following equation: $\begin{matrix}{R_{2} = {\frac{\left( {\frac{\alpha_{2}}{\alpha_{1}} + {\frac{\alpha_{3}}{\alpha_{1}}\gamma}} \right)}{\left( {{\omega^{2}\gamma^{2}} + \frac{1}{s^{2}}} \right)}.}} & (57)\end{matrix}$

The rotor current and torque can be calculated using the followingequations:I ₂={square root}{square root over (α₁ ²+β₁ ²)}.  (58)

The torque T may be estimated by: $\begin{matrix}{{{T\quad\left( {{in}\quad\text{Newton-meters}} \right)} = \frac{3*I_{2{rms}}^{2}*R_{2}}{\omega_{2}*S}};} & (59)\end{matrix}$where $\omega_{s} = \frac{4\quad\pi\quad f}{p}$is the synchronous speed and p is the number of poles. To convert thetorque to ft-lbs multiply the T in Newton-meters by 0.738.

For the purpose of calculating motor efficiency the output power needsto be calculated. This can be obtained using the following equation:$\begin{matrix}{{{{Output}\quad{Power}\quad P_{out}} = {\frac{TN}{5252} - P_{{F\&}W} - {SLL}}};} & (60)\end{matrix}$

-   -   where, T is shaft torque in ft-lb and SLL is the stray load        power loss, which is typically a known percentage motor power        depending on motor size and varies with the square of the        torque. The IEEE standard specifies certain percentage of output        power as SLL. This percentage changes as the motor power        changes. For example, for 1 to 125 HP motors, the SLL is equal        to 1.8% of maximum power. For 126 to 500 HP motors, the SLL is        equal to 1.5% of maximum power. Finally, for 501 to 2499 HP        motors, the SLL is equal to 1.2% of maximum power.

As mentioned above, if the friction and windage loss is not known, itsvalue can be lumped with the core loss. The effect of lumping thefriction and windage loss with core loss is to cause the rotor loss tobe lower than the actual loss, thus raising the estimated efficiency,since the effect of lumping the friction and windage loss with the coreloss is to reduce the power across the air gap by the friction andwindage loss. In this circumstance, the rotor loss is the motor sliptimes the friction and windage loss. To obtain an estimate of themaximum error using this approximation, a value of slip equal to 0.025and a maximum percentage of friction and windage loss of motor powerequal to 3% may be used. This yields a maximum error in estimating theefficiency equal to 0.075 %, which is within the measurement error.Tests conducted on different motors indicate the validity of theassumption. If the value of the friction and windage loss is known, thenthat value may be used. The motor efficiency may then be estimated usingthe ratio of the estimated output power to the input power. Theabove-described method was applied to experimental data and the resultsindicate an accuracy of over 99%.

It is important to note that the core loss is obtained at a constantfrequency. If the motor used at a different frequency, then the coreloss needs to be estimated at the new frequency. In general the coreloss is proportional to the square of frequency and to the magnitude ofthe flux density. If the flux density is constant then a simple equationcan be used to estimate the core loss at a different operatingfrequency.

Test Results:

The no-load data from three motors were used to test the accuracy of theabove method. The following is a summary of the data obtained. 10 HPMotor: Motor Data: HP: 10 Elec. Des.: E9893A A RPM: 1175 Frame: 0256TEnclosure: TEFC Design: B Volts: 575 LR Code: G Amp: 10.1 Rotor:418138071HE Duty: Cont. Stator: 418126002AJ INS/AMB/S.F.: F/40/1.15 FAN:702675001A TYP/PH/HZ: P/3/60 No load Current:  4.41 ampere No LoadVoltage:  574.9 volts No Load Power: 261.73 watts Stator Resistance:0.8765 ohm F&W power:    57 watts Stray Load Loss: 1.13% obtained fromexperimental data

The results obtained are as follows: Actual Motor Efficiency at fullload = 90.2434% Estimated Motor Efficiency = 90.8452% Estimation Error = 0.6357% 150 HP Motor: Motor Data: HP: 150 Elec. Des.: W00868-A-A001RPM: 1180 Frame: EC360 Enclosure: TENV Volts: 460 Amp: 10.1 Duty: 15 MinINS/AMB/S.F.: F/ /1.15 No Load Current:  66.09 ampere No Load Voltage:   460 volts No Load Power:   2261 watts Stator resistance: 0.03509 ohmF & W power:    896 watts Stray Load Loss: 0.85% from test data

The results obtained are as follows: Actual Motor Efficiency at fullload = 93.106% Estimated Motor Efficiency = 93.413% Estimation Error =0.3303% 600 HP Motor: Motor Data: HP: 600 Elec. Des.: RPM: 1195 Frame:35C5012Z Enclosure: TEFC Design: 139481 Volts: 575 LR Code: Amp: 532Rotor: 710623-2-S Duty: Cont. Stator: 710622-2-T INS/AMB/S.F.: F/ /1.15No Load Current = 148.45 ampere No Load Voltage =   575 volts No LoadPower =   6860 watts Stator resistance =  .0091 ohm F & W power =   1725watts Stray Load Loss = 1.3% from Test data

The results obtained are as follows: Actual Motor Efficiency at fullload = 96.025% Estimated Motor Efficiency = 95.976% Estimation Error =−0.0500% 

To make the estimation of the motor efficiency less sensitive to slighterrors in measured frequency, the following process may be performed.First, the stator loss is calculated using the input current and theestimated stator resistance R₁. The friction and windage loss isestimated based on the motor size, type, and speed. The rotor loss maybe estimated by subtracting the stator loss from the Input power P andmultiplying the remainder by the slip. The stray load loss SLL isestimated based on the IEEE standard, as described above, with theexception that the core loss is neglected. The modified input power isthen calculated at the two measurement points by subtracting the abovelosses from the input power P.

A plot of the modified input power versus measured speed may then beperformed to determine the core loss. The core loss is the modifiedinput power at the synchronous speed n_(s). This can be determinedmathematically using the following equation: $\begin{matrix}{{{CoreLoss} = {\left( {P_{1} - {n_{1}\left( \frac{P_{2} - P_{1}}{n_{2} - n_{1}} \right)}} \right) + {\left( \frac{P_{2} - P_{1}}{n_{2} - n_{1}} \right)n_{s}}}};} & (61)\end{matrix}$where:

-   -   P₁ Modified Input power at point 1 “low load”    -   P₂ Modified Input power at point 2 “high load”    -   n₁ Motor speed at point 1    -   n₂ Motor speed at point 2    -   n_(s) Synchronous speed using the measured frequency at low        load.

The rotor loss and the stray load loss SLL may then be recalculatedusing the new core loss value. The magnetizing inductance L_(m), rotorresistance R₂, and rotor leakage inductance L₂ are calculated asprovided previously. This method was found to be less sensitive to errorin frequency measurements.

The temperature of the rotor during motor operation may be estimatedusing the estimated value of the rotor resistance R₂ and the followingequation relating changes in electrical resistance of the rotor tochanges in temperature:R _(2hot) =R _(2cold)(1+α(T _(hot) −T _(cold)));  (62)where: R_(2 cold) is the rotor resistance at a first temperature;R_(2 hot) is the rotor resistance at a second temperature; T_(cold) isthe rotor temperature at a first temperature; T_(hot) is the rotortemperature at a second temperature; and α is the temperaturecoefficient of electrical resistance of the rotor in Ω/unit oftemperature.

As an example, the above equation may be manipulated algebraically toobtain the following equation for an aluminum rotor: $\begin{matrix}{T_{hot} = {{\frac{R_{2{hot}}}{R_{2{cold}}}*\left( {255 + T_{cold}} \right)} - 225.}} & (63)\end{matrix}$The value used for R_(2 hot) is the estimated value for the rotorresistance R₂ at the second temperature T_(hot). The control module 90may be used to input the rotor temperature at the first temperatureT_(cold) and the rotor resistance at the first temperature R_(2 cold).In addition, the data may be provided by the remote stations 98 via thenetwork 96.

Referring generally to FIG. 7, a process for establishing values ofvarious motor electrical parameters and various motor operatingparameters using the system of FIG. 3 is shown and designated generallyby reference numeral 130. The process comprises obtaining the resistanceof the stator, as represented by block 132. The process also comprisesobtaining data at a single operating load point and providing the datato the processor module 84, as represented by block 134. In a presentlycontemplated embodiment, the data obtained at the first load pointcomprises: input voltage data, input current data, input power data,shaft speed data, and stator temperature data. It should be noted thatthe input power can either be measured or calculated from the otherinput data. Some data may be provided to the system 80 using the controlmodule 90 or may be provided from a remote station 98 via the network96.

As represented by block 136, the data processing module 82 then operatesto establish estimated values of various motor parameters. As discussedabove, these estimated motor parameters may comprise one or more of thecircuit parameters in the motor equivalent circuits 50 and 110illustrated in FIGS. 2 and 5. Accordingly, the various motor parametersmay comprise the stator resistance R₁, the slip s, the stator leakagereactance X₁, the rotor resistance R₂, the rotor leakage reactance X₂,the core loss resistance R_(c), and the magnetizing reactance X_(m). Thestator resistance R₁ and the motor slip s can be measured relativelyeasily, while the remaining parameters (i.e., X₁, R₂, X₂, R_(c), andX_(m)) are estimated by the processor module 84 in accordance withunique aspects of the process 130 illustrated in FIG. 7.

As represented by block 138, the data processing module 82 then operatesto establish estimated values of other unknown motor parameters based onthe one or more parameters estimated in block 136. For example, the dataprocessing module 82 may estimate output power, efficiency, torque, andother characteristics of the motor 20. Accordingly, in certainembodiments, the data processing module 82 operates in accordance withthe process 130 to obtain various losses associated with the motor 20.For example, the losses may comprise stator loss, rotor loss, core loss,friction and windage, and stray load loss. The stator loss can beestimated accurately by measuring the stator resistance R₁ and thestator current I₁. The friction and windage loss can be estimated usingsimulated data on different motor sizes. For example, the dataprocessing module 82 can access a database of motors to obtain theappropriate friction and windage loss. An exemplary motor database maylist the motor frame size, number of poles, fan diameter, and the lossassociated with the motor. The stray load loss can be estimated usingthe IEEE standard. Finally, data processing module 82 estimates therotor loss and the core loss, as described in further detail below.

The rotor loss can be estimated approximately by multiplying the inputpower minus the stator loss by the slip, as follows:RotorLoss=(P _(in)−3I ₁ ² R ₁)s  (64)P_(in) is the input power in watts, I₁ is the input current, R₁ is thestator phase resistance, and s is the slip of the rotor. As discussedabove with reference to FIG. 7, these parameters are obtained in blocks132 and 134 of the process 130. Accordingly, the data processing module82 readily estimates the rotor loss according to equation (64). Theerror in estimating the rotor loss using this method is equal to theslip s multiplied by the core loss. In view of the equivalent circuit 50of FIG. 2, the core loss can be expressed as follows: $\begin{matrix}{{CoreLess} = \frac{3V_{a}^{2}}{R_{c}}} & (65)\end{matrix}$V_(a) is the voltage across the rotor and R_(c) is the core lossresistance. Accordingly, the error associated with the rotor losscalculated above in equation (64) can be expressed as follows:$\begin{matrix}{{{Rotor}\quad{Loss}\quad{Error}} = {\frac{3V_{a}^{2}}{R_{c}}s}} & (66)\end{matrix}$The foregoing calculation provides an accurate estimation of rotor lossfor motors having low to moderate core loss (e.g., less than 50% of thetotal losses). For example, if the core loss (65) is roughly 20% of thelosses, then a motor having 85% efficiency will have a core loss ofapproximately the 3% of the input power. If the motor has four poles anda 40-rpm slip at full load, then the slip s will be approximately0.0227. Applying these values to equation (66), the percentage error inrotor loss is equal to 0.068% of input power. Accordingly, the rotorloss error (66) has a negligible effect on the calculation of rotor loss(64) and motor efficiency, as discussed in further detail below.

The only loss left to be estimated is the core loss. For this estimatedmotor parameter, the data processing module 82 operates to calculate thevarious parameters of the equivalent circuits 50 and 110, as illustratedin FIGS. 2 and 5. In the illustrated embodiment of FIG. 7, the dataprocessing module 82 operates to obtain or estimate the variousparameters: R₁, s, X₁, R₂, X₂, R_(c), and X_(m). The calculation of thestator resistance R₁ and the motor slip s can be obtained relativelyeasily. However, the data processing module 82 estimates the remainingparameters (i.e., X₁, R₂, X₂, R_(c), and X_(m)) using unique aspects ofthe process 130, as set forth below. Once all circuit parameters areobtained, the data processing module 82 estimates the core loss. Inturn, the data processing module 82 can estimate other operatingparameters of the motor, such as motor efficiency, torque, and so forth.

As discussed above, the process 130 comprises several assumptions andapproximations to simplify the process of estimating X₁, R₂, X₂, R_(c),and X_(m). For example, the frequency of the power is assumed to beconstant, the speed of the rotor is assumed to be constant during thegathering of the single load point data, and the rotor temperature isassumed to be constant during the gathering of the data. Additionally,it has been shown that the stator leakage reactance X₁ can be expressedas a fraction of the magnetizing reactance X_(m) using the followingequation:X ₁=0.0325X _(m)  (67)As discussed above, this factor may range from 0.02 to 0.07.

According to the IEEE standard, the rotor leakage reactance X₂ can beexpressed as a function of the stator leakage reactance X₁ as follows:For design A motors: X₂=X₁  (68)For design B motors: X ₂=1.492X ₁  (69)For design C motors: X ₂=2.325X ₁  (70)For design D motors: X₂=X₁  (71)Accordingly, the calculation of rotor leakage reactance X₂ provided byequations (68) through (71) depends on the calculation of stator leakagereactance X₁ provided by equation (67), which in turn depends on thecalculation of magnetizing reactance X_(m). The magnetizing reactanceX_(m) is estimated by the data processing module 82, as set forth below.

In view of the simplified motor equivalent circuit 110 illustrated inFIG. 5, the data processing module 82 estimates an approximate value ofequivalent resistance X_(e) using the following equations relating themeasured input current, voltage and power: $\begin{matrix}{{{Real}\quad{Part}\quad{of}\quad{Input}\quad{Impedance}\quad Z_{inR}} = \frac{V_{inR}}{I_{1}}} & (72) \\{{{Imaginary}\quad{Part}\quad{of}\quad{input}\quad{Impedance}\quad Z_{inI}} = \frac{V_{inI}}{I_{1}}} & (73) \\{X_{e} = {\left( {X_{inI} - X_{1}} \right) + \frac{\left( {Z_{inR} - R_{1}} \right)^{2}}{\left( {Z_{inI} - X_{1}} \right)}}} & (74)\end{matrix}$V_(inR) is the real portion of the input voltage, V_(inI) is theimaginary portion of the input voltage, I₁ is the electric currentthrough the stator, R₁ is the stator resistance, and X₁ is the statorleakage reactance. The data processing module 82 also defines theparallel resistive element or total resistance R_(t), as set forth inthe following equation: $\begin{matrix}{R_{t} = {\left( {Z_{inR} - R_{1}} \right) + \frac{\left( {Z_{inI} - X_{1}} \right)^{2}}{\left( {Z_{inR} - R_{1}} \right)}}} & (75)\end{matrix}$In this exemplary embodiment, the data processing module 82 initiallyassumes the stator leakage reactance X₁ equal to zero to estimate afirst approximation of the equivalent resistance X_(e), as set forthbelow: $\begin{matrix}{{X_{e}({approximate})} = {Z_{inI} + \frac{\left( {Z_{inR} - R_{1}} \right)^{2}}{Z_{inI}}}} & (76)\end{matrix}$

In view of the relationships set forth above in equations (67) through(76), the data processing module 82 estimates an approximate value forthe stator leakage reactance X₁ as a fraction of the first approximationof the equivalent resistance X_(e), as follows:X ₁(approximate)=0.0325X _(e)(approximate)  (77)Again, this factor may range from 0.02 to 0.07. After calculating anapproximate value for the stator leakage reactance X₁ as set forth byequation (77), the data processing module 82 can estimate the rotorleakage reactance X₂ using the appropriate one of equations (68) through(71). Accordingly, only the rotor resistance R₂, the core lossresistance R_(c), and the magnetizing reactance X_(m) remain to beestimated by the data processing module 82.

In the illustrated embodiment of FIG. 7, data processing module 82estimates the rotor resistance R₂ using the following relationships:$\begin{matrix}{R_{2} = \frac{3V_{a}^{2}s^{2}}{RotorLoss}} & (78)\end{matrix}$Again, V_(a) is the voltage across the rotor, s is the slip of therotor, and the rotor loss is estimated according to equation (64) Therotor voltage V_(a) can be calculated from the real and imaginary partsV_(aR) and V_(aI) of the rotor voltage V_(a), as set forth in thefollowing equations:V _(aR) =V _(1R) −I ₁ R ₁  (79)V _(aI) =V _(1I) −I ₁ X ₁  (80)V _(a)=(V _(aR) ² +V _(aI) ²)^(1/2)  (81)After calculating the rotor voltage V_(a), the data processing module 82proceeds to calculate the rotor resistance defined by equation (77).Accordingly, only the core loss resistance R_(c) and the magnetizingreactance X_(m) remain to be estimated by the data processing module 82.

The data processing module 82 can calculate the magnetizing reactanceX_(m) and that core loss resistance R_(c) from the followingrelationships: $\begin{matrix}{\frac{1}{X_{e}} = \frac{1}{X_{m} + \frac{1}{X_{2} + \frac{R_{2}^{2}}{X - 2}}}} & (82) \\{\frac{1}{R_{t}} = {\frac{1}{R_{c}} + \frac{1}{\frac{R_{2}}{S} + \frac{X_{2}^{2}}{\frac{R_{2}}{S}}}}} & (83)\end{matrix}$Finally, using the core loss resistance R_(c) calculated from equation(83), the processing module 82 can calculate the core loss defined byequation (65).

At this point, the data processing module 82 has estimated values forall of the motor parameters (e.g., X₁, R₂, X₂, R_(c), and X_(m)) and allthe motor losses (e.g., stator loss, rotor loss, core loss, friction andwindage loss, and stray load loss). If desired, after calculating themagnetizing reactance X_(m) as set forth in equation (82), the dataprocessing module 82 can recalculate the stator leakage reactance X₁according to equation (67). In turn, the data processing module 82 canrecalculate the other motor parameters (e.g., R₂, X₂, R_(c), and X_(m))and the core loss using the newly estimated value of stator leakagereactance X₁. Accordingly, the data processing module 82 can reiteratethe calculations set forth in equations (67) through (83) any number oftimes to improve the accuracy of the estimated motor parameters.

After obtaining final estimations of these motor parameters and losses,the data processing module 82 can proceed to estimate motor operatingparameters, such as motor efficiency, torque, and so forth (block 138).For example, the system may be adapted to calculate the rotor torque,the rotor temperature, and the motor efficiency based on the values ofR₂, X₂, R_(c), and X_(m), electrical input data, and rotor speed data.As discussed above, the shaft torque may be obtained from the rotorresistance R₂ and the rotor current I₂ as set forth in equation (24). Inaddition, the motor efficiency can be estimated from the followingequation: $\begin{matrix}{\eta = {\frac{P_{out}}{P_{in}} = \frac{P_{in} - {SL} - {RL} - {CL} - {FWL} - {SLL}}{P_{in}}}} & (84)\end{matrix}$SL is the stator loss, RL is the rotor loss estimated above in equation(64), CL is the core loss estimated above in equation (65), FWL is thefriction and windage loss, and SLL is the stray load loss.

The process 130 described above with reference to FIG. 7 provides anexceptional estimation of the motor parameters, motor losses, and themotor efficiency. These estimations are particularly accurate if thecore loss moderate to low, e.g., less than 50% of the total motorlosses. The reason for this correlation between accuracy and core lossis due to the assumption of zero core loss in the estimation of rotorloss, rotor resistance R₂, and core loss resistance R_(C). In theillustrated embodiment of FIG. 7, the magnitude of the core lossresistance R_(C) relates to the addition of the rotor leakage reactanceX₂. Accordingly, the value of the rotor leakage reactance X₂ results ina different core loss resistance R_(C).

As an example of the accuracy of the single load point techniquesdescribed above, the process 130 was used to estimate the efficiency ofa 60 HP motor. The actual efficiency of the motor is 94.4%, whereas theprocess 130 estimated the motor efficiency as 94% using a single loadpoint. In addition, a TENV 75 HP motor (design B) was evaluated usingboth the two load points and single load point techniques described withreference to FIGS. 4 and 7. The motor efficiency estimated according tothe two load points technique was 90.6%, while the single load pointtechnique yielded a motor efficiency of 91.6%. The single load pointtechnique of FIG. 7 estimated motor efficiencies based on the high loadpoint and different reactance ratios X₂/X₁, i.e., 1.5, 2, 2.5, and 3, astabulated below: Reactance Ratio Core Resistance Ohm Efficiency 1.5 31691.6 2   158 90.7 2.5 90.6 89.26 3   56.1 87.25 Zero Core Loss Max Eff.Infinity 92.6At a reactance ratio of 1.5, the motor efficiency estimated by thesingle point technique of FIG. 7 is approximately 1% higher than themotor efficiency estimated by the two point technique of FIG. 4.Accordingly, it can be concluded that the single point technique of FIG.7 estimates the motor efficiency at an accuracy of 98%, because theaccuracy of the two point technique of FIG. 4 has been established atapproximately 99%. As a result, the single point technique of FIG. 7 canprovide a range of motor efficiencies by estimating the maximumefficiency based on zero core loss and a lower bound using a leakagereactance ratio of 2.5.

Referring generally to FIG. 8, a process for establishing values ofvarious motor electrical parameters and various motor operatingparameters using the system of FIG. 3 is shown and designated generallyby reference numeral 140. The process comprises obtaining data at afirst operating load point and providing the data to the processormodule 84, as represented by block 142. The process also comprisesobtaining data at a second operating load point and providing the datato the processor module 84, as represented by block 144. The processfurther comprises obtaining data at a third operating load point andproviding the data to the processor module 84, as represented by block146. In a presently contemplated embodiment, the data obtained at thefirst, second, and third load points comprises: input voltage data,input current data, input power data, shaft speed data, and frequency ofthe motor 20. It should be noted that the input power can either bemeasured or calculated from the other input data. In addition, theprocess may measure motor temperature. However, the data obtained atthese three points generally does not include the stator resistance ofthe motor 20. Some data may be provided to the system 80 using thecontrol module 90 or may be provided from a remote station 98 via thenetwork 96.

As represented by block 148, the data processing module 82 then operatesto establish estimated values of various motor parameters without theneed to measure the stator resistance. As discussed above, theseestimated motor parameters may comprise one or more of the circuitparameters in the motor equivalent circuits 50 and 110 illustrated inFIGS. 2 and 5. Accordingly, the various motor parameters may comprisethe stator resistance R₁, the slip s, the stator leakage reactance X₁,the rotor resistance R₂, the rotor leakage reactance X₂, the core lossresistance R_(c), and the magnetizing reactance X_(m). These sevenparameters determine the motor equivalent circuit 50. Accordingly, themotor equivalent circuit 50 can be fully analyzed by measuring and/orestimating these parameters. The motor slip s can be calculated based onthe speed of the motor, which is obtained in blocks 142, 144, and 146.The remaining parameters (i.e., R₁, X₁, R₂, X₂, R_(c), and X_(m)) areestimated by the processor module 84 in accordance with unique aspectsof the process 140 illustrated in FIG. 8.

As represented by block 150, the data processing module 82 then operatesto establish estimated values of other unknown motor parameters based onthe one or more parameters estimated in block 148. For example, the dataprocessing module 82 may estimate output power, efficiency, torque, andother characteristics of the motor 20. In addition, in certainembodiments, the data processing module 82 operates in accordance withthe process 140 to obtain various losses associated with the motor 20.For example, the losses may comprise stator loss, rotor loss, core loss,friction and windage, and stray load loss. Based on these losses, thedata processing module 82 can then estimate the motor efficiency.

To estimate the six unknown motor parameters, the process 140 of FIG. 8proceeds to solve six equations relating to measurements of the inputvoltage, current, power, and output speed at the three load points. Inview of the motor equivalent circuit 50 of FIG. 2, the input impedanceat three load points may be defined by the following equations:$\begin{matrix}{Z_{in1} = {Z_{2} + \frac{Z_{c}Z_{r1}}{Z_{c} + Z_{r1}}}} & (85)\end{matrix}$ $\begin{matrix}{Z_{in2} = {Z_{s} + \frac{Z_{c}Z_{r2}}{Z_{c} + Z_{r2}}}} & (86) \\{Z_{in3} = {Z_{s} + \frac{Z_{c}Z_{r3}}{Z_{c} + Z_{r3}}}} & (87)\end{matrix}$Z_(s) is the stator impedance, Z_(c) is of the core impedance, and Z_(r)is the rotor impedance. These three input impedance equations can becombined by subtracting equation (86) from equation (85), subtractingequation (87) from equation (85), and dividing the resulting twoequations to obtain the following: $\begin{matrix}{\frac{\left( {Z_{in1} - Z_{in2}} \right)\left( {Z_{c} + Z_{r2}} \right)}{\left( {Z_{in1} - Z_{in3}} \right)\left( {Z_{c} + Z_{r3}} \right)} = \frac{\left( {Z_{r1} - Z_{r2}} \right)}{\left( {Z_{r1} - Z_{r3}} \right)}} & (88)\end{matrix}$In addition, given that the rotor leakage inductance L₂ and the rotorresistance R₂ are the same at each of the three load points, the righthand side of equation (88) can be simplified to the following equation:$\begin{matrix}{\lambda = \frac{\left( {\frac{1}{S_{1}} - \frac{1}{S_{2}}} \right)}{\left( {\frac{1}{S_{1}} - \frac{1}{S_{3}}} \right)}} & (89)\end{matrix}$S₁, S₂, and S₃ are the motor slips at the three load points. Asdiscussed above, these motor slips S₁, S₂, and S₃ can be calculated fromspeed measurements obtained in blocks 142, 144, and 146 of the process140. Denoting the quantity in equation (89) by λ, the foregoing equation(88) can be solved for core impedance Z_(c) in terms of the rotorimpedance Z_(r) at load points 2 and 3 as set forth in the followingequation: $\begin{matrix}{Z_{c} = \frac{{\left( {Z_{in1} - Z_{in2}} \right)Z_{r2}} - {{\lambda\left( {Z_{in1} - Z_{in3}} \right)}Z_{r3}}}{\left\lbrack {{\lambda\left( {Z_{in1} - Z_{in3}} \right)} - \left( {Z_{in1} - Z_{in2}} \right)} \right\rbrack}} & (90)\end{matrix}$

The core impedance Z, defined by equation (90) can then be substitutedinto equation (88) to obtain an equation in the rotor input impedancesZ_(r1), Z_(r2) and Z_(r3) at the first, second, and third load points.These rotor input impedances Z_(r1), Z_(r2) and Z_(r3) are functions ofthe rotor leakage reactance X₂ and the motor resistance R₂. Theresulting equation can be decomposed into a real part and an imaginarypart yielding two equations in the two rotor unknowns. The rotorimpedance Z_(r) can be expressed as: $\begin{matrix}{Z_{r} = {\frac{R_{2}}{S} + {jX}_{2}}} & (91)\end{matrix}$Using equation (91) at the three load points yields the rotor impedanceZ_(r) at the three different slips S₁, S₂, and S₃. After the foregoingsubstitution of the core impedance Z_(c) decomposition into real andimaginary parts, equation (88) can be redefined as set forth below:The real part is given by: $\begin{matrix}{{{\left( {\frac{A_{22}}{S_{2}^{2}} + \frac{A_{33}}{S_{3}^{2}} + \frac{A_{12}}{S_{1}S_{2}} + \frac{A_{13}}{S_{1}S_{3}} + \frac{A_{23}}{S_{2}S_{3}}} \right)R_{2}^{2}} - {\left( {A_{22} + A_{33} + A_{12} + A_{13} + A_{23}} \right)X_{2}^{2}} - {\left\lbrack {\frac{2B_{22}}{S_{2}} + \frac{2B_{33}}{S_{3}} + {\left( {\frac{1}{S_{1}} + \frac{1}{S_{2}}} \right)B_{12}} + {\left( {\frac{1}{S_{1}} + \frac{1}{S_{3}}} \right)B_{13}} + {\left( {\frac{1}{S_{2}} + \frac{1}{S_{3}}} \right)B_{23}}} \right\rbrack R_{2}X_{2}}} = 0} & (92)\end{matrix}$The imaginary part is given by: $\begin{matrix}{{{\left( {\frac{B_{22}}{S_{2}^{2}} + \frac{B_{33}}{S_{3}^{2}} + \frac{B_{12}}{S_{1}S_{2}} + \frac{B_{13}}{S_{1}S_{3}} + \frac{B_{23}}{S_{2}S_{3}}} \right)R_{2}^{2}} - {\left( {B_{22} + B_{33} + B_{12} + B_{13} + B_{23}} \right)X_{2}^{2}} - {\left\lbrack {\frac{2A_{22}}{S_{2}} + \frac{2A_{33}}{S_{3}} + {\left( {\frac{1}{S_{1}} + \frac{1}{S_{2}}} \right)A_{12}} + {\left( {\frac{1}{S_{1}} + \frac{1}{S_{3}}} \right)A_{13}} + {\left( {\frac{1}{S_{2}} + \frac{1}{S_{3}}} \right)A_{23}}} \right\rbrack R_{2}X_{2}}} = 0} & (93)\end{matrix}$The A's and the B's in equations (92) and (93) are functions of themeasured input impedance at the three load points and, also, the rotorresistance R₂.

As set forth below in detail below, these two equations (92) and (93)can be simplified as:(M ₁ +M ₂ R ₂)R ₂ ²+(N ₁ +N ₂ R ₂)X ₂ ²+(L ₁ +L ₂ R ₂)R ₂ X ₂=0  (94)(U ₁ +U ₂ R ₂)R ₂ ²+(V ₁ +V ₂ R ₂)X ₂ ²+(W ₁ +W ₂ R ₂)R ₂ X ₂=0  (95)Equation (95) essentially obtains the rotor leakage reactance X₂ interms of the rotor resistance R₂. The A's and B's can be defined by thefollowing equations in which β_(R) and β_(j) are the real and imaginaryparts of the measured differential input impedance β₁ and β₂ and thesubscripts 1, 2, and 3 refer to the first, second, and third load pointsobtained at blocks 142, 144, and 146 of the process 140 of FIG. 7.$\begin{matrix}{A_{22} = {{\left( {\beta_{1R}^{2} - \beta_{1j}^{2}} \right)\left( {{\left( {\frac{1}{S_{2}} - \frac{1}{S_{1}}} \right)R_{2}} + {\lambda\quad\beta_{2R}}} \right)} - {2\quad\beta_{1R}\beta_{1j}\beta_{2j}\lambda}}} & (96) \\{\beta_{1} = {Z_{in1} - Z_{in2}}} & (97) \\{\beta_{2} = {Z_{in1} - Z_{in3}}} & (98) \\{A_{33} = {\lambda^{2}\left\lbrack {{\left( {\beta_{2R}^{2} - \beta_{2j}^{2}} \right)\left( {{\left( {\frac{1}{S_{2}} - \frac{1}{S_{1}}} \right)R_{2}} + \beta_{1R}} \right)} - {2\quad\beta_{2R}\beta_{2j}\beta_{1j}}} \right\rbrack}} & (99) \\{A_{12} = \begin{bmatrix}{{\left( {{\beta_{1R}\beta_{2R}} - {\beta_{1j}\beta_{2j}}} \right)\left( {{\lambda^{2}\beta_{2R}} - {\lambda\quad\beta_{1R}}} \right)} -} \\{\left( {{\beta_{1R}\beta_{2j}} + {\beta_{1j}\beta_{2R}}} \right)\left( {{\lambda^{2}\beta_{2j}} - {\lambda\quad\beta_{1j}}} \right)}\end{bmatrix}} & (100) \\{A_{13} = {- A_{12}}} & (101) \\{A_{23} = {- \begin{bmatrix}\left( {{\beta_{1R}\beta_{2R}} - {\beta_{1j}\beta_{2j}}} \right) \\{\left( {{\lambda\quad\beta_{1R}} + {\lambda^{2}\beta_{2R}} + {2{R_{2}\left( {\frac{1}{S_{1}} - \frac{1}{S_{2}}} \right)}}} \right) -} \\{\left( {{\beta_{1R}\beta_{2j}} + {\beta_{1j}\beta_{2R}}} \right)\left( {{\lambda\quad\beta_{1j}} + {\lambda^{2}\beta_{2j}}} \right)}\end{bmatrix}}} & (102) \\{B_{22} = {{\lambda\quad{\beta_{2j}\left( {\beta_{1R}^{2} - \beta_{1j}^{2}} \right)}} + {2\beta_{1R}{\beta_{1j}\left( {{\left( {\frac{1}{S_{2}} - \frac{1}{S_{1}}} \right)R_{2}} + {\lambda\quad\beta_{2R}}} \right)}}}} & (103) \\{B_{33} = {\lambda^{2}\left\lbrack {{\beta_{1j}\left( {\beta_{2R}^{2} - \beta_{2j}^{2}} \right)} + {2\quad\beta_{2R}{\beta_{2j}\left( {{\left( {\frac{1}{S_{2}} - \frac{1}{S_{1}}} \right)R_{2}} + \beta_{1R}} \right)}}} \right\rbrack}} & (104) \\{B_{12} = \begin{bmatrix}{{\left( {{\beta_{1R}\beta_{2j}} + {\beta_{1j}\beta_{2R}}} \right)\left( {{\lambda^{2}\beta_{2R}} - {\lambda\quad\beta_{1R}}} \right)} +} \\{\left( {{\beta_{1R}\beta_{2R}} - {\beta_{1j}\beta_{2j}}} \right)\left( {{\lambda^{2}\beta_{2j}} - {\lambda\quad\beta_{1j}}} \right)}\end{bmatrix}} & (105) \\{B_{13} = {- B_{12}}} & (106) \\{B_{23} = {- \begin{bmatrix}{{\left( {{\beta_{1R}\beta_{2R}} - {\beta_{1j}\beta_{2j}}} \right)\left( {{\lambda\quad\beta_{1j}} + {\lambda^{2}\beta_{2j}}} \right)} +} \\\left( {{\beta_{1R}\beta_{2j}} + {\beta_{1j}\beta_{2R}}} \right) \\\left( {{\lambda\quad\beta_{1R}} + {\lambda^{2}\beta_{2R}} + {2{R_{2}\left( {\frac{1}{S_{1}} - \frac{1}{S_{2}}} \right)}}} \right)\end{bmatrix}}} & (107)\end{matrix}$

In turn, an equation (108) can be achieved by dividing equations (94)and (95) by the square of the rotor leakage reactance X₂ ² and bydefining α=R₂/X₂ (i.e., the ratio of rotor resistance R₂ to rotorleakage reactance X₂), as set forth below: $\begin{matrix}{\alpha = \frac{\begin{matrix}{{\left( {W_{1} + {W_{2}R_{2}}} \right)\left( {N_{1} + {N_{2}R_{2}}} \right)} -} \\{\left( {L_{1} + {L_{2}R_{2}}} \right)\left( {V_{1} + {V_{2}R_{2}}} \right)}\end{matrix}}{\begin{matrix}{{\left( {M_{1} + {M_{2}R_{2}}} \right)\left( {V_{1} + {V_{2}R_{2}}} \right)} -} \\{\left( {N_{1} + {N_{2}R_{2}}} \right)\left( {U_{1} + {U_{2}R_{2}}} \right)}\end{matrix}}} & (108)\end{matrix}$

In view of the equations set forth above, the rotor leakage reactance X₂can be obtained in terms of the rotor resistance R₂ based on equation(95). The rotor leakage reactance X₂ from equation (108) can then besubstituted into the equation (94). This substitution yields a cubicequation in the rotor resistance R₂. Using a spreadsheet, it was foundthat the foregoing equation reduces to a quadratic equation in the rotorresistance R₂. Accordingly, after solving for the rotor resistance R₂,the rotor leakage reactance X₂ can be obtained using equation (108). Inturn, the core impedance Z_(c) can be obtained using equation (90).Moreover, the stator impedance can then be obtained using equation (85).If desired, the data processing module 82 can calculate other parametersbased on the foregoing calculations. For example, the data processingmodule 82 uses these estimated parameters to estimate the efficiency ofthe motor 20.

The process 140 described above with reference to FIG. 8 was evaluatedwith data obtained at three load points on a real motor. The process 140provided exceptionally accurate estimations of motor efficiency.Numerical analysis and the foregoing tests indicated an estimation errorof approximately 1.5% as it pertains to the estimation of motorefficiency. A portion of this error can be attributed to inaccuraciesencountered in the field due to instrumentation.

Referring generally to FIG. 9, a process for establishing values ofvarious motor electrical parameters and various motor operatingparameters, such as motor torque and speed, is shown and designatedgenerally by reference numeral 160. The process 160 comprises obtainingbaseline motor parameters and providing the data to the processor module84, as represented by block 162. For example, the data processing module82 may obtain the various parameters for the motor equivalent circuits50 and 110 of FIGS. 2 and 5 at a particular baseline condition. Incertain embodiments, as described below, the baseline condition maycomprise a motor frequency (e.g., 60 Hz) for an inverter-driven motor.If desired, the process 160 may employ any one of the processes 100,120, 130, or 140 described above with reference to FIGS. 4, 6, 7, and 8.The process 160 also comprises obtaining motor data at a desiredoperating load point or condition (e.g., a new motor frequency otherthan baseline) and providing the data to the processor module 84, asrepresented by block 164. In a presently contemplated embodiment, thedata obtained at the desired operating load comprises: input voltagedata, input current data, input power data, shaft temperature data, andfrequency data of the motor 20. It should be noted that the input powercan either be measured or calculated from the other input data. Inaddition, the data obtained at these three points generally does notinclude the speed and/or torque of the motor 20. Some data may beprovided to the system 80 using the control module 90 or may be providedfrom a remote station 98 via the network 96.

As represented by block 166, the data processing module 82 then operatesto establish estimated values of various motor parameters at the desiredoperating load based on the baseline motor parameters and the dataobtained at the desired operation load. Again, this estimation step 166may be performed without measurements of the speed and/or torque of themotor 20. As discussed above, these estimated motor parameters maycomprise one or more of the circuit parameters in the motor equivalentcircuits 50 and 110 illustrated in FIGS. 2 and 5. Accordingly, thevarious motor parameters may comprise the stator resistance R₁, the slips, the stator leakage reactance X₁, the rotor resistance R₂, the rotorleakage reactance X₂, the core loss resistance R_(c), and themagnetizing reactance X_(m). These seven parameters determine the motorequivalent circuit 50. Accordingly, the motor equivalent circuit 50 canbe fully analyzed by measuring and/or estimating these parameters. Asdiscussed below, the data processing model 82 estimates these parametersin accordance with unique aspects of the process 160 illustrated in FIG.9.

As represented by block 168, the data processing module 82 then operatesto establish estimated values of other unknown motor parameters based onthe one or more parameters estimated in block 166. For example, the dataprocessing module 82 may estimate output power, speed, efficiency,torque, and other characteristics of the motor 20. In addition, incertain embodiments, the data processing module 82 operates inaccordance with the process 160 to obtain various losses associated withthe motor 20. For example, the losses may comprise stator loss, rotorloss, core loss, friction and windage, and stray load loss.

Returning to block 166, the process 160 estimates the stator leakageinductance L₁ and the rotor leakage inductance L₂ to be equal to theinductances obtained at the baseline condition. In this manner, themotor parameters L₁ and L₂ are assumed constant. Regarding resistances,the process 160 estimates the stator resistance R₁ and the rotorresistance R₂ as a function of temperature. For example, the statorresistance R₁ can be calculated based on the baseline temperatureT_(baseline), the baseline stator resistance R_(baseline), and thecurrent stator temperature T at the desired operating load, as set forthbelow: $\begin{matrix}{R = {\frac{\left( {234.5 + T} \right)}{\left( {234.5 + T_{baseline}} \right)}R_{baseline}}} & (109)\end{matrix}$Accordingly, only three unknown motor parameters remain to be estimatedby the process 160.

The series core loss resistance R_(m) can be calculated according to thefollowing equation: $\begin{matrix}{R_{m} = {R_{m60}\left( {{{.8}\left( \frac{f}{60} \right)} + {{.2}\left( \frac{f}{60} \right)^{2}}} \right)}} & (110)\end{matrix}$In the above equation (110), f is the input frequency and R_(m60) is theseries core loss resistance, which is known at the baseline condition ofthe motor. For example, in this particular embodiment, the series coreloss resistance R_(m60) corresponds to a baseline input frequency of 60Hz. Accordingly, only two unknown motor parameters (i.e., L_(m) and s)remain to be estimated by the process 160.

To estimate the two unknown motor parameters, the process 160 of FIG. 9proceeds to solve two equations using the baseline motor parameters andthe data obtained at the desired operating load (e.g., input current,voltage, power, and frequency). Based on the measurement of inputcurrent, the input current complex value can be calculated as set forthbelow:I _(in) =I _(inR) +j _(inI)  (111)Subscripts R and I represent the real and imaginary parts of the inputcurrent I_(in). Using the equivalent circuit of the induction motor, theprocess 160 can express the input current I_(in) in terms of the motorinput phase voltage and the equivalent circuit impedance. First, theinput impedance can be expressed as:Z _(in) =Z _(inR) +jZ _(inI)  (112)In real and imaginary parts, the process 160 can express the inputimpedance of equation (112) as follows: $\begin{matrix}{Z_{in} = \frac{\begin{bmatrix}{\left\lbrack {{R_{1}\left( {{R_{2}/s} + R_{m}} \right)} - {X_{1}\left( {X_{2} + X_{m}} \right)}} \right\rbrack +} \\{j\left\lbrack {{R_{1}\left( {X_{2} + X_{m}} \right)} + {X_{1}\left( {{R_{2}/s} + R_{m}} \right)}} \right\rbrack}\end{bmatrix}}{\left( {{R_{2}/s} + R_{m}} \right) + {j\left( {X_{2} + X_{m}} \right)}}} & (113)\end{matrix}$Accordingly, in terms of the input phase voltage and input impedance,the process 160 can express the input current I_(in) as set forth below:$\begin{matrix}{I_{in} = \frac{V}{Z_{inR} + {jZ}_{in1}}} & (114)\end{matrix}$In turn, the process 100 can express the foregoing equation (114) as setforth in the following equation: $\begin{matrix}{{I_{inR} + {jI}_{inI}} = {{V\left( \frac{Z_{inR}}{Z_{inR}^{2} + Z_{inI}^{2}} \right)} - {{jV}\left( \frac{Z_{inI}}{Z_{inR}^{2} + Z_{inI}^{2}} \right)}}} & (115)\end{matrix}$

In view of the baseline parameters and the data and parameters at thedesired operating load, the process 160 can equate the real parts andthe imaginary parts on both sides of equation (115) to obtain twoequations corresponding to the baseline and the desired operating load.Given that the only unknown parameters are the magnetizing reactanceX_(m) and the slip s, the process 160 can calculate the values of themagnetizing reactance X_(m) and the slip s at the desired operatingload. Using the calculated slip s and the measured frequency f theprocess 160 can calculate the speed (e.g., rotations per minute) of themotor. In addition, the process 160 can calculate other motor operatingparameters, such as torque, efficiency, output power, and so forth. Forexample, the motor torque can be calculated according to equation (24),as discussed above. Moreover, given that output power is related to theoutput speed times the torque, the process 160 can calculate the outputpower using the output torque and speed of the motor. The process 160can then calculate the new motor efficiency as set forth in equation(26), as discussed above. In this manner, the process 160 facilitatesthe identification of motor operating parameters without implementing aspeed sensor and/or a torque sensor.

Referring generally to FIG. 10, a system for establishing values ofvarious motor electrical parameters and various motor operatingparameters is shown and designated generally by reference numeral 200.As illustrated, the system 200 comprises the control module 90 and thedata processing module 82, which can be separate or integral componentsof a variety of mobile or stationary systems, electronic devices,instruments, computers, software programs, circuit boards, and so forth.The illustrated embodiment of the data processing module 82 comprises avariety of modules or features to facilitate the estimation ofelectrical and operating parameters of the motor 20. Each of thesemodules may comprise software programs or components, hardwarecircuitry, and so forth. For example, the data processing module 82 maycomprise one or more of the following features: a no-load motorestimation module 202, a single load point motor estimation module 204,a two load point motor estimation module 206, a three load point motorestimation module 208, a baseline-load motor estimation module 210, thedata processor module 84, one or more databases of motor losses 212(e.g., friction and windage loss database), one or more databases ofnew/replacement motors 213, one or more databases of customer motors214, a data storage and access module 216, a motor resistance processingmodule 218, an energy analysis module 220, and/or a monetary analysismodule 222. Although other features also may be incorporated into thedata processing module 82 of system 200, the foregoing modules may beemployed to provide exceptionally accurate estimations of electrical andoperating parameters of the motor 20, as described below.

Regarding modules 202 through 210, the no-load motor estimation module202 may comprise one or more of the various features described abovewith reference to the process 120 illustrated by FIG. 6. Similarly, thesingle load point motor estimation module 204 can have one or more ofthe features described above with reference to the process 130illustrated by FIG. 7. With reference to FIG. 4, the two load pointmotor estimation module 206 may incorporate one or more of the featuresdescribed above with reference to the process 100. The three load pointmotor estimation module 208 can employ one or more of the featuresdescribed with reference to the process 140 illustrated by FIG. 8.Finally, the baseline-load motor estimation module 210 may comprise oneor more of the various features described above with reference to theprocess 160 illustrated by FIG. 9.

Regarding the databases 212 through 214, the system 200 may store theinformation locally or remotely on one or more storage devices,computers, instruments, networks, and so forth. Accordingly, thedatabases 212 through 214 may be readily available on a local storagedevice or the system 200 may communicate with a remote device over anetwork, such as the network 96 illustrated by FIG. 3. Turning now tothe specific databases, the database of motor losses and parameters 212may comprise a variety of motor information, such as motor frame size,number of poles, fan diameter, and various losses associated with themotor. For example, the motor losses may comprise the friction andwindage loss for various motors. Accordingly, the database 212 can beaccessed and queried to obtain the desired data, such as the motorlosses. For example, if the system 200 is estimating output power oroperational efficiency, then the motor losses (e.g., friction andwindage loss) can be obtained from the database 214 to facilitate a moreaccurate estimation of these operating parameters.

As discussed in further detail below, the database of new/replacementmotors 213 can be used by the system 200 to evaluate and compareexisting motors against the benefits of a new/replacement. For example,the database 213 may comprise a variety of operational parameters, suchas motor efficiency, power usage, torque, space consumption, and soforth. Accordingly, the data processing module 82 may compare this motordata against estimated operational parameters of an old motor, such asthe motor 20 being evaluated by the system 200.

The database have customer motors 214 also may comprise a variety ofelectrical and operational parameters for various motors. For example,each motor at a customer's site can be recorded in the database 214according to motor efficiency, horsepower, application or use, locationwithin the site, and various other features of the motor. In addition,the database 214 can store performance data taken at various times overthe life of the motor, such that trends or changes in motor performancecan be identified and addressed by customer. The database 214 also canbe organized in various data sheets according to motor type,application, location, date of test, efficiency, and other features.Again, the particular data stored in the database 214 may compriseelectrical parameters (e.g., resistances, inductances, etc.),operational parameters of the motor (e.g., efficiency, torque, etc.),power usage, time usage, costs, age, specification information,servicing, maintenance, testing, and so forth.

In addition to the databases, the illustrated system 200 comprises thedata storage and access module 216, which has a data logging module 224,a data identification module 226, and a data population module 228. Inoperation, the data logging module 224 records various motor data andmeasurements, such as input current, voltage, frequency, power, time ofmeasurement (e.g., date, clock time, and duration), speed, and othermotor parameters. For example, the data logging module 224 may storetest results according to a file name, a test time, and/or anotheridentifying parameter (e.g., a motor speed). In turn, the dataidentification module 226 facilitates retrieval of the recorded dataaccording to one or more identifying parameters. For example, if thesystem 200 engages one of the motor estimation modules 202 through 210,then the data storage access module 216 may utilize the dataidentification module 226 to identify the appropriate data for use inestimating motor parameters. In certain embodiments, this may involvedata entry or selection of a filename, a testing time, a type ofmeasurement, or another identifier. The data storage access module 216can then engage the data population module 228, which retrieves theidentified motor data and populates the appropriate fields with themotor data. For example, the data population module 228 may populatedata fields in one of the motor estimation modules 202 through 210 withmotor parameters corresponding to input voltage, current, frequency,power, and/or a variety of other motor data. The data population module228 also may populate one or more visual forms, spreadsheets, formulas,and other functional or visual objects with the identified data. As aresult, the data storage and access module 216 reduces errors associatedwith data logging, retrieval, and use by the system 200, while alsoimproving the overall efficiency of the system 200 by automating thesefunctions.

As illustrated, the motor resistance processing module 218 comprises atemperature compensation module 230, a data entry module 232, and aresistance calculation module 234. As described below, these modules230, 232, and 234 facilitate automatic calculation of the motorresistance parameters based on various data input. In this manner, themotor resistance processing module 218 improves the efficiency of thesystem 200, reduces errors associated with motor resistancecalculations, and improves the accuracy of the motor resistance valuesfor use by the motor estimation modules 202 through 210. For example,the illustrated temperature compensation module 230 uses a baselinemeasurement of motor temperature and stator resistance to adjust thestator resistance as the motor temperature changes. In operation, thetemperature compensation module 230 may employ the followingrelationship between stator resistance and temperature for copper:$\begin{matrix}{R_{t2} = {\frac{\left( {234.5 + T_{2}} \right)}{\left( {234.5 + T_{1}} \right)}{R_{t1}.}}} & (116)\end{matrix}$In this equation (116), T₁ refers to the baseline motor temperature, T₂refers to the current motor temperature, R_(t1) refers to the baselineresistance of the stator, and R_(t2) refers to the currenttemperature-compensated value of the stator resistance. The data entrymodule 232 also cooperates with the temperature compensation module 230to obtain the baseline motor temperature T₁, the baseline statorresistance R_(t1), and the current motor temperature T₂ to calculate thecurrent resistance R_(t2) according to equation (116). In addition, theresistance calculation module 234 comprises or more formulas orequations to facilitate the calculation of resistance (e.g., cableresistance) based on various motor data or parameters. For example, theresistance calculation module 234 may cooperate with the data entrymodule 232 to obtain a cable gauge, a number of cables for phase, acable length, a cable temperature, and other desired parameters tocalculate the desired motor resistance. As a result, the motorresistance processing module 218 reduces errors associated with usercalculations, improves the overall efficiency of the system 200 byautomating these calculations, and improves the accuracy of resistancevalues for use by the motor estimation modules 202 through 210.

Turning now to the energy and monetary analysis modules 220 and 222, thesystem 200 may engage these modules to evaluate the performance of themotor 20 and compare this performance against one or morenew/replacement motors, such as those stored in the database ofnew/replacement motors 213. As illustrated, the energy analysis module220 comprises an energy usage module 236 and an energy savings module238. In operation, the energy usage module 236 calculates or estimatesthe overall energy usage of the motor 20, while the energy savingsmodule 238 calculates or estimates any energy savings that may beobtained by replacing the existing motor 20 with a new/replacementmotor. For example, the energy savings module 238 may evaluate a varietyof motors having different levels of energy efficiency and otherperformance criteria. As result, a customer can make an informeddecision whether to replace the motor 20 with a new/replacement motor.

In addition, the monetary analysis module 222 may function cooperativelywith or separately from the energy analysis module 220. In thisexemplary embodiment, the monetary analysis module 222 comprises a costanalysis module 240 and a savings analysis module 242. For example, thecost analysis module 240 may calculate the monetary cost of the motor 20based on the output power, the cost per kilowatt-hour, and the number ofhours per week of operation of the motor 20. Similarly, the savingsanalysis module 242 may calculate the monetary cost of a new/replacementmotor and then calculate the monetary difference between thenew/replacement motor and the existing motor 20. As result, a customercan make an informed decision whether to replace the motor 20 with anew/replacement motor.

While the invention may be susceptible to various modifications andalternative forms, specific embodiments have been shown by way ofexample in the drawings and have been described in detail herein.However, it should be understood that the invention is not intended tobe limited to the particular forms disclosed. Rather, the invention isto cover all modifications, equivalents, and alternatives falling withinthe spirit and scope of the invention as defined by the followingappended claims.

1. A system for estimating parameters of a motor, the system comprising:an electronic device that is operable to establish estimated values of aplurality of electrical parameters of an electric motor based onelectrical input data obtained at a single load point of the electricmotor.
 2. The system as recited in claim 1, wherein the electronicdevice is operable to establish an estimated value of an operatingparameter of the electric motor based on the estimated values ofelectrical parameters of the electric motor.
 3. The system as recited inclaim 2, wherein the operating parameter is motor torque.
 4. The systemas recited in claim 2, wherein the operating parameter is motorefficiency.
 5. The system as recited in claim 2, wherein the operatingparameter is rotor temperature.
 6. The system as recited in claim 1,wherein the plurality of electrical parameters of the electric motorcomprises electrical resistance of the rotor during operation of theelectric motor.
 7. The system as recited in claim 1, wherein theplurality of electrical parameters of the electric motor comprisesstator inductance.
 8. The system as recited in claim 1, wherein theelectrical input data comprises input voltage, input current, and inputfrequency.
 9. The system as recited in claim 8, wherein the electricalinput data comprises motor temperature and motor speed.
 10. The systemas recited in claim 8, wherein the electrical input data comprises inputpower.
 11. The system as recited in claim 8, wherein the electronicdevice is operable to establish input power from the input current andthe input voltage.
 12. The system as recited in claim 1, comprising avisual display operable to provide a visual indication of at least oneof the estimated values of a plurality of electrical parameters and theestimated value of an operating parameter.
 13. The system as recited inclaim 1, comprising a communication module operable to enable data to bemanually provided to the system.
 14. The system as recited in claim 1,wherein the electronic device is coupleable to an externalcommunications network.
 15. An electric motor system for estimating aparameter of a motor, the system comprising: an electronic device thatis operable to establish an estimated value of an operating parameter ofan electric motor based on electrical input data obtained at first,second, and third load points of the electric motor.
 16. The system asrecited in claim 15, wherein the electronic device comprises a dataprocessing module adapted to estimate the operating parameter without ameasurement of stator resistance of the electric motor.
 17. The systemas recited in claim 15, wherein the operating parameter comprises motorefficiency.
 18. The system as recited in claim 15, wherein the operatingparameter comprises motor torque.
 19. The system as recited in claim 15,wherein the operating parameter comprises motor output power.
 20. Thesystem as recited in claim 15, wherein the operating parameter comprisesrotor temperature.
 21. The system as recited in claim 15, wherein theelectrical input data comprises input voltage, input current, and speedof the electric motor.
 22. The system as recited in claim 21, whereinthe electrical input data comprises motor temperature and frequency ofthe electric motor.
 23. The system as recited in claim 22, wherein theelectrical input data comprises input power of the electric motor. 24.The system as recited in claim 22, wherein the electronic device isoperable to establish input power of the electric motor.
 25. A systemfor estimating parameters of a motor, the system comprising: anelectronic device that is operable to establish estimated values of aplurality of electrical parameters of an inverter-driven electric motorbased on baseline motor parameters and based on electrical input dataobtained at a desired operating condition of the inverter-drivenelectric motor, wherein baseline motor parameters comprise a first motorfrequency and the desired operating condition comprises a second motorfrequency.
 26. The system as recited in claim 25, wherein the electronicdevice is operable to establish an estimated value of at least oneoperating parameter of the inverter-driven electric motor based on theestimated values.
 27. The system as recited in claim 25, wherein thebaseline motor parameters define an equivalent circuit of theinverter-driven electric motor.
 28. The system as recited in claim 25,wherein the first motor frequency is approximately 60 Hertz.
 29. Thesystem as recited in claim 25, wherein the electronic device comprises amotor estimation module adapted to establish a core loss resistance atthe desired operating condition based at least partially on a change inmotor frequency.
 30. The system as recited in claim 25, wherein theelectrical input data comprises input voltage, input current, inputfrequency, and temperature.
 31. The system as recited in claim 25,comprising a visual display and a keyboard.
 32. A system for estimatingparameters of a motor, the system comprising: means for obtainingelectrical parameters of an electric motor based on electrical inputdata of the electric motor; and means for estimating at least oneoperating parameter of the electrical motor based at least partially onthe means for obtaining electrical parameters.
 33. The system as recitedin claim 32, wherein the means for obtaining electrical parameterscomprises means for estimating at least one of the electrical parametersbased at least partially on motor parameters measured at a single loadpoint of the electric motor.
 34. The system as recited in claim 32,wherein the means for obtaining electrical parameters comprises meansfor estimating at least one of the electrical parameters based at leastpartially on motor parameters measured at three load points of theelectric motor.
 35. The system as recited in claim 32, wherein the meansfor obtaining electrical parameters comprises means for estimating atleast one of the electrical parameters based at least partially onbaseline motor parameters and motor parameters measured at a desiredoperating load point of the electric motor.
 36. The system as recited inclaim 32, wherein the means for estimating at least one operatingparameter comprises means for estimating operating efficiency of theelectric motor.
 37. The system as recited in claim 32, wherein the meansfor estimating at least one operating parameter comprises means forestimating output power of the electric motor.
 38. The system as recitedin claim 32, wherein the means for estimating at least one operatingparameter comprises means for estimating torque of the electric motor.39. The system as recited in claim 32, wherein the means for estimatingat least one operating parameter comprises means for estimating rotortemperature of the electric motor.
 40. The system as recited in claim32, wherein the means for estimating at least one operating parametercomprises means for estimating performance of the electric motor.
 41. Amachine readable medium for analyzing an electric motor, comprising: amotor estimation module stored on the machine readable medium andadapted to establish estimated values of a plurality of electricalparameters of the electric motor based at least partially on measuredmotor parameters, wherein the motor estimation module is adapted toestimate an operating parameter of the electric motor based at leastpartially on the estimated values.
 42. The machine readable medium asrecited in claim 41, wherein the motor estimation module comprises asingle load point motor estimation module adapted to estimate theplurality of electrical parameters based on motor measurements at asingle load of the electric motor.
 43. The machine readable medium asrecited in claim 41, wherein the motor estimation module comprises athree load point motor estimation module adapted to estimate theplurality of electrical parameters based on motor measurements at first,second, and third loads of the electric motor.
 44. The machine readablemedium as recited in claim 41, wherein the motor estimation modulecomprises a baseline and load point motor estimation module adapted toestimate the plurality of electrical parameters based on baseline motorparameters and motor measurements at a desired operating load of theelectric motor, wherein the baseline motor parameters comprise a firstmotor frequency and the desired operating load comprises a second motorfrequency different from the first motor frequency.
 45. (canceled) 46.The machine readable medium as recited in claim 45, wherein theoperating parameter comprises efficiency of the electric motor.
 47. Themachine readable medium as recited in claim 45, wherein the operatingparameter comprises torque of the electric motor.
 48. The machinereadable medium as recited in claim 45, wherein the operating parametercomprises power output of the electric motor.
 49. The machine readablemedium as recited in claim 45, wherein the operating parameter comprisesrotor temperature of the electric motor.
 50. A motor analysis device,comprising: a data processing module comprising a plurality of motorestimation modules adapted to estimate parameters of an electric motorbased on input parameters, which are at least partially different foreach of the plurality of motor estimation modules.
 51. The motoranalysis device as recited in claim 50, wherein the plurality of motorestimation modules comprises a single load point motor estimation moduleadapted to estimate a plurality of electrical parameters of the electricmotor based on motor measurements at a single load point of the electricmotor.
 52. The motor analysis device as recited in claim 50, wherein theplurality of motor estimation modules comprises a three load point motorestimation module adapted to estimate a plurality of electricalparameters of the electric motor based on motor measurements at first,second, and third load points of the electric motor.
 53. The motoranalysis device as recited in claim 50, wherein the plurality of motorestimation modules comprises a baseline and load point motor estimationmodule adapted to estimate a plurality of electrical parameters of theelectric motor based on baseline motor parameters and motor measurementsat a desired operating load of the electric motor, wherein the baselinemotor parameters comprise a first motor frequency and the desiredoperating load comprises a second motor frequency different from thefirst motor frequency.
 54. The motor analysis device as recited in claim50, wherein the plurality of motor estimation modules are adapted toestimate an operational performance parameter of the electric motorbased at least partially on the estimated parameters.
 55. A method ofanalyzing a motor having a rotor and a stator, comprising: providing aninstrumentation system with stator resistance data for the motor;providing the instrumentation system with output speed and electricalinput data obtained during operation of the motor at a single load pointof the motor; and operating the instrumentation system to establishestimated values of a plurality of electrical parameters of the motorbased on the stator resistance data and the electrical input data. 56.The method as recited in claim 55, wherein providing the instrumentationsystem with output speed and electrical input data comprises obtaininginput current, input voltage, frequency, and stator temperature of themotor at the single load point.
 57. The method as recited in claim 55,further comprising operating the instrumentation system to estimate atleast one motor operating performance parameter based on the estimatedvalues and the electrical input data.
 58. A method of operating a motorhaving a rotor and a stator, comprising: providing an instrumentationsystem with motor speed and electrical input data obtained duringoperation of the motor with first, second, and third loads on the motor;and operating the instrumentation system to establish estimated valuesof a plurality of electrical parameters of the motor based on the motorspeed and electrical input data obtained during operation of the motorwith the first, second, and third load points on the motor.
 59. Themethod as recited in claim 58, wherein providing the instrumentationsystem with motor speed and electrical input data comprises obtaininginput current, input voltage, and frequency of the motor at the first,second, and third load points.
 60. The method as recited in claim 58,further comprising operating the instrumentation system to estimate atleast one motor performance parameter based on the estimated values, themotor speed, and the electrical input data.
 61. A method of operating aninverter-driven motor, comprising: providing an instrumentation systemwith baseline parameters of the inverter-driven motor at a firstfrequency; providing the instrumentation system with electrical inputdata obtained for the inverter-driven motor operating at a secondfrequency; and operating the instrumentation system to establish anestimated operational parameter of the inverter-driven motor based onthe baseline parameters and the electrical input data.
 62. The method asrecited in claim 61, wherein providing the instrumentation system withelectrical input data comprises obtaining input current, input voltage,frequency, and temperature of the motor at the desired operating load.63. The method as recited in claim 61, wherein operating theinstrumentation system to establish the estimated operational parametercomprises estimating output speed of the motor.
 64. The method asrecited in claim 61, wherein operating the instrumentation system toestablish the estimated operational parameter comprises estimatingtorque of the motor.
 65. The method as recited in claim 61, whereinoperating the instrumentation system to establish the estimatedoperational parameter comprises estimating output power of the motor.66. The method as recited in claim 61, wherein operating theinstrumentation system to establish the estimated operational parametercomprises estimating efficiency of the motor.
 67. The method as recitedin claim 61, wherein operating the instrumentation system to establishthe estimated operational parameter comprises establishing a core lossresistance at the second frequency as a function of the second frequencyand a baseline core loss resistance at the first frequency.